Question

Find the initial value P, growth/decay factor a, and growth/decay rate r for the following exponential function:Help me solve part C! Q(t) = 1625(1.22)^t(a) The initial value is P= 1625(b) The growth factor is a = 1.22(c) The growth rate is r=(Note that if r gives a decay rate you should have r < O.)

Answer 1

Given the exponential function:

`Q(t)=16.25(1.22)^t`

Let's find the initial value P, growth /decay factor a, and growth/decay rate r.

Aply the general exponential formula:

`f(x)=P(1\pm r)^t`

Here, we have:

P = 16.25

Growth factor, a = 1.22

If the factor is less than 1 it is an exponential decay function.

If the factor is greater than 1, it is an exponential growth function.

To find the value of r, we have:

1 + r = 1.22

r = 1.22 - 1.0

r = 0.22

Therefore, the growth rate is 0.22 or 22%.

ANSWER:

(c). The growth rate is r = 0.22