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Write an exponential function to model this situation: a population of 420 animals decreases at an annual rate of 21%. Then predict the value of the function after 5 years (to the nearest whole number).

User PrashanD
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2 Answers

4 votes

Answer:


y=420\cdot (0.79)^x

The value of the function after 5 years would be 129.

Explanation:

We have been that a population of 420 animals decreases at an annual rate of 21%. We are asked to write an exponential function for our given problem.

We know that an exponential function is in form
y=a\cdot b^x, where,

a = Initial value,

b = For decay b is in form
1-r, where, r represents decay rate in decimal form.


r=21\%=(21)/(100)=0.21


y=a\cdot (1-r)^x


y=420\cdot (1-0.21)^x


y=420\cdot (0.79)^x

Therefore, our required function would be
y=420\cdot (0.79)^x.

To find the value of the function after 5 years, we will substitute
x=5 in our function.


y=420\cdot (0.79)^5


y=420\cdot 0.3077056399


y=129.236368758


y\approx 129

Therefore, the value of the function after 5 years would be 129.

User Josh Grosso
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6 votes
Here is the answer to the given problem above.
Here is the exponential function to model this situation:
f(x) = 420(0.79)x
Now, solve with the given values.
P(t)=420×(.79)^t P(5)=420×(.79)^5=129
So the answer would be 129 animals.
Hope this answer helps. Thanks for posting your question!
User Alexander Trust
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