A species of animal is discovered on an island. Suppose that the population size P(t) of the species can be modeled by the following function, where time t is measured in years.
P(t) =800/1+ 3e^-0.29t.
Find the initial population size of the species and the population size after 10 years. Round your answers to the nearest whole number as necessary.
Answer:
The initial population is 200
The population after 10 years is 687
Step-by-step explanation:
Given
[tex]P(t) =\frac{800}{1+ 3e^{-0.29t.}}[/tex]
Solving (a): The initial population
Here:
[tex]t = 0[/tex]
Substitute 0 for t in P(t)
[tex]P(0) =\frac{800}{1+ 3e^{-0.29*0}}[/tex]
[tex]P(0) =\frac{800}{1+ 3e^{0}}[/tex]
[tex]P(0) =\frac{800}{1+ 3*1}[/tex]
[tex]P(0) =\frac{800}{1+ 3}[/tex]
[tex]P(0) =\frac{800}{4}[/tex]
[tex]P(0) =200[/tex]
The initial population is 200
Solving (b): Population after 10 years.
Here
[tex]t = 10[/tex]
Substitute 10 for t in P(t)
[tex]P(10) =\frac{800}{1+ 3e^{-0.29*10}}[/tex]
[tex]P(10) =\frac{800}{1+ 3e^{-2.9}}[/tex]
[tex]P(10) =\frac{800}{1+ 3*0.055}[/tex]
[tex]P(10) =\frac{800}{1+ 0.165}[/tex]
[tex]P(10) =\frac{800}{1.165}[/tex]
[tex]P(10) =687[/tex] -- approximated.
The population after 10 years is 687
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Gabriel saves 40% of his monthly paycheck for college. He earned $270 last month. How much money did Gabriel save for college?
A $108
B $96
C $162
D $180
ASAP PLEASEEE
Answer:
A $108
Step-by-step explanation:
40% = .4
.4 * 270 = 108
Mylo started making this graph to relate the number of hours he works with the amount of money he is paid. A point representing which information could be added to the graph to show a proportional relationship? A. $16 for working 2 hours B. $36 for working 4 hours C. $40 for working 5 hours D. $58 for working 6 hours\
Answer:
I can confirm that the awnser is B
Step-by-step explanation:
I got a 100%
Answer:
B
Step-by-step explanation:
the other person said it was B
Help please!
Urgent Question!!!
Step-by-step explanation:
Coordinates of Point R = (0, y).
We have PR = QR.
=> (-2 - 0)² + (6 - y)² = (9 - 0)² + (3 - y)².
=> 4 + (6 - y)² = 81 + (3 - y)²
=> y² - 12y + 40 = y² - 6y + 90
=> 6y + 50 = 0
=> y = -25/3.
Hence the answer is (0, -25/3).
Coordinates of Point S = (x, 0).
We have PS = QS.
=> (-2 - x)² + (6 - 0)² = (9 - x)² + (3 - 0)²
=> (-2 - x)² + 36 = (9 - x)² + 9
=> x² + 4x + 40 = x² - 18x + 90
=> 22x = 50
=> x = 25/11.
Hence the answer is (25/11, 0).
here,
coordinates of P(-2,3)
coordinates of Q(9,3)
coordinates of R(0,0)
now,
PR=QR
or, 0-(-2)+0-3=(0-9)+(0-3)
or, 2-3= -9-3
or, -1 = -12
ok so this is fraction what is 5/6 x 3/4
Answer:
5/8
Step-by-step explanation:
The temperature was -12 degrees
Celsius and rose to 2 degrees Celsius.
What was the change in temperature?
Hurry
Answer:
+14 degrees Celsius
Step-by-step explanation:
you have to find the difference from -12 to 2 degree Celsius
Graph and find the area of the figure with the vertices (-3, 0), (1,4), (2, 0)
Answer:
10
Step-by-step explanation:
A farm has 5 brown cows and 10 white cows. A fence is open and a cow escapes. What is the probability that it will be a brown cow?
Answer:
D
Step-by-step explanation:
HELP PLEASE...........
Answer:
1. 9
2. 12
3. 26
Step-by-step explanation:
Answer:
1. 9
2. 12
3. 26
Step-by-step explanation:
An easy way to solve problems like this is to convert the percentage into a decimal, then multiply that decimal by the whole. For example, if I had the question "What is 10% of 100?", I would first convert the 10% to a decimal. 10% is the same as 10/100, which in decimal form is 0.1. I would then multiply 0.1 by 100 to find out how much 10% of 100 is. I get 10, so my answer is 10. Hope this helps!
4 2/3 divided by 1/2 in fraction form
Answer:
9 1/3
Step-by-step explanation:
4 2/3 = 14/3
14/3/1/2
14/3 x 2/1
28/3= 9 1/3
Can someone please explain how to do number 9.
Answer:
x<15, probably
Step-by-step explanation:
maybe multiply 2 to each side to eliminate the fraction. so 3x+15<60. subtract 15 to isolate the variable term so 3x<45. divide by 3 to isolate x so x<15. check the work. is the inequality true for all values of x less than 15? let's try the first possible integer value, 14, to be sure. 3(14)+15= 57. so 57/2<30. now 57/2 is 28.5 and 28.5<30 so it seems right
one of sam's best customer spend 250.00 each month in sam's shop. She say that is roughly 5% of her monthly income. How much does she make each month.
Answer:
5,000
Step-by-step explanation:
x× 5 %=250
x=250×100÷5=5000
A principal of $2600 is invested at 3% Interest, compounded annually. How much will the investment be worth after 14 years
Answer:
3692
Step-by-step explanation:
Multiply the starting amount, by the percent, and them multiply by how many years (2600*0.03%*14)
the rate of change of sales tax on trousers is 10% one can buy a pair of trousers at$660. What is the marked price?
Step-by-step explanation:
Total price = Marked price + Sales tax
= Marked price + (0.1 * Marked price)
= 1.1 * Marked price.
Since the total price is $660, the marked price is $660 / 1.1 = $600.
Help plz:)))I’ll mark u Brainliest
Answer:
The answer to the question provided is
[tex] \frac{9}{5} [/tex]
Will mark brainliest!!!solve for each variable
1. How could you find the actual number of sticky notes it will take to cover the cabinet, excluding the bottom? What information would you need to know?
Hey there!
You would probably need to know the dimensions and surface area of the cabinet, and the dimensions and area of the sticky notes.
Hope it helps and have an amazing day!
Find the distance from the point (0, 3) to the line y = 3x – 9. Round your answer to the nearest tenth.
The distance is about
units.
Answer:
4
Step-by-step explanation:
This is a vague question so I understand why you reached out for help. Please not that my answer is not correct in case the problem is subliminally asking for the shortest distance, but there is no indication of that on the question prompt.
The graph is not drawn to scale.
The distance between the line and the point is 4 units.
What is Distance formula?The formula to find the distance between the two points is usually given by d=√((c-a)² + (d-b)²). This formula is used to find the distance between any two points on a coordinate plane or x-y plane.
Given: line: y= 3x-9
put y= 3
3 = 3x-9
12 = 3x
x= 4
and, the other point is (0, 3).
Now, the distance between theses points
D= √(4-0)² + (3 -)²
D= √4²
D= √16
D= 4 units
Hence, the distance is 4 units.
Learn more about Distance formula here:
https://brainly.com/question/1872885
#SPJ2
x2 – 12x + 37 = 0 in simplest a + bi form
Answer:
x=6+1
Step-by-step explanation:
Marking brainiest
Jessica melts 200 grams of dark chocolate that contains 60% cocoa and mixes it with 200 grams of milk chocolate that contains 30% cocoa
What is the concentration of cocoa in the resulting mixture?
Answer:
45%
Step-by-step explanation:
200g milk chocolate
200g dark chocolate
= 400g of chocolate
x = the %
x/100 = 180/400
18000 = 400x
x = 45
45%
1. What does the algebraic representation (x,y) → (x-1, y-2) represent?
A Each point of a figure will translate 1 unit left and 2 units down.
B Each point of a figure will translate 1 unit left and 2 units up
. C Each point of a figure will translate 1 unit right and 2 units up.
D Each point of a figure will translate I unit right and 2 units down.(their is no visual)
Answer:
A) Each point will translate 1 unit left and 2 units down
Step-by-step explanation:
I got it right in my test Answer A
Solve for x
5x + 2 = 17
Answer:
r
Step-by-step explanation:
r
Answer:
Step-by-step explanation:
Here you go mate
Step 1
5x+2=17 Equation/Question
Step 2
5x+2=17 Simplify
5x+2=17
Step 3
5x+2=17 Subtract 2
5x=15
Step 4
5x=15 Divide
answer
x=3
Hope this helps
Determine the smallest integer value of x in the solution of the following inequality.
-x-2≤5
Answer:
Step-by-step explanation:
Here you go mate
Step 1
-x-2≤5 Equation/Question
Step 2
-x-2≤5 Simplify
-x≤7
Step 3
-x≤7 Divide
answer
x≥-7
Miya is selling grapefruit and nuts for a fundraiser. The grapefruits cost 5 dollars each and a bag of nuts cost 15 dollars each. She sells 30 items and made 250 dollars. How many grapefruits did she sell?
Answer:
A) 5G + 15N = 250
B) G + N = 30 We'll multiply B) by -5
B) -5G -5N = -150 then we add A)
A) 5G + 15N = 250
10N = 100
N = 10 bags of nuts ($150.00)
We put N=10 into A)
A) 5G + 150 = 250
A) 5G = 100
G = 20 Grapefruits ($100.00)
Step-by-step explanation:
What is the slope of the line that passes through the points (4, 7) and (5,8)?
Write your answer in simplest form.
Answer:
1
Step-by-step explanation:
Use the coordinates of the points to determine the slope
slope = Δy/Δx = (8-7)/(5-4) = 1
y = |cosx|
any body can answer my question
Which statement describes why AABC and ADEF are congruent by SAS?
Answer:It is The first one.
Step-by-step explanation:
9x+ 5 = 14x — 4
I need help with this I have to solve for x
Answer:
here u go
Step-by-step explanation:
its 9/5 or 1.8. Also 1 to 4/5
Plz help. I rally need it
Answer:
8
Step-by-step explanation: