Answer:

y=420cdot (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=acdot 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=acdot (1-r)^x

y=420cdot (1-0.21)^x

y=420cdot (0.79)^x

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

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

y=420cdot (0.79)^5

y=420cdot 0.3077056399

y=129.236368758

yapprox 129

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