Question

a population of 430 animals decreases at an annual rate of 21% find the multiplier for the rate of exponential decay

Answer 1

0.79

Explanation:

We have been given that a population of 430 animals decreases at an annual rate of 21%. We are asked to find the multiplier for the rate of exponential decay.

We know that an exponential decay function is in form
`y=a\cdot (1-r)^x`, where,

a = Initial value,

r = Decay rate in decimal form.

Let us convert 21% in decimal form as:

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

Upon substituting our given values, we will get:

`y=430\cdot (1-0.21)^x`

`y=430\cdot (0.79)^x`

Therefore, the multiplier for the rate of exponential decay is 0.79.

Answer 2

If the population of the animals decreases by about 21% of its current population, it means that the population next year is only 1 - 0.21 or 0.79 of its current population. Thus, the multiplier for the rate of the exponential decay is 0.79.