Question

A population of insects, in thousands, can be molded using the function (t)= 1.75(0.97)x

Answer 1

Question:

A population of insects, in thousands, can be modeled using the function

`p(t) = 1.75(0.97)^t`, where t is time in months. Which statement best

describes the population of insects?

A. The population is decaying at a rate of 3% each month.

B. The population is decaying at a rate of 25% each month.

C. The population is growing at a rate of 75% each month.

D. The population is growing at a rate of 97% each month.

Answer:

A. The population is decaying at a rate of 3% each month.

Explanation:

Given

`p(t) = 1.75(0.97)^t`

Required

True statement about the function

From the options, we can see that we are to answer the question on the basis of decay and growing rates.

An exponential form is:

`y=ab^x`

Compare to
`p(t) = 1.75(0.97)^t`

`b= 0.97\\`

If
`b > 1`, then
`b = 1 + r` r represents growth rate

else,
`b= 1-r` r represents decay rate

Since b < 0.97:

`0.97= 1-r`

`r = 1 - 0.97`

`r = 0.03`

`r = 3\%`

`r = 0.03`