Question

Identify the initial amount a and the rate of growth r (as a percent) of the exponential function. Evaluate the function when t = 5. Round your answer to the nearest tenth.

h(t) =
`8.1^(t)`

Answer 1

The initial value is 1 and growth factor as a percentage will be 710%.

Explanation:

The exponential growth function is given by
`f(x) = a (b)^(x)` ......... (1), where, a is called as the initial value and b is called as the growth factor.

Now, in this case the the function is given to be
`h(t) = 8.1^(t)` ....... (2)

Now, comparing equation (1) and (2), we get

a = 1 and b = 8.1

Now, b = 1 + r

⇒ 8.1 = 1 + r

⇒ r = 7.1

So, the initial value is 1 and growth factor as a percentage will be 7.1 × 100 % = 710%. (Answer)