Web Analytics
Answered

Is my answer correct?

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).

Verified Answer :

metchelle

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!

Answer:

\(y=420\cdot (0.79)^x\)

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

Step-by-step 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.

\(r=21\%=\frac{21}{100}=0.21\)

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

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

\(y=420\cdot (0.79)^x\)

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.