All exponential functions can be written in many forms. Write the function f, of, t, equals, 30000, e, start superscript, 0, point, 1, 2, t, end superscriptf(t)=30000e

Question

0.12t
in the form f, of, t, equals, a, b, start superscript, 15, t, end superscriptf(t)=ab
15t
. Round all coefficients to four decimal places.

Answer 1

The given exponential function is:

f(t) = 30000e^(0.12t)

To write it in the form f(t) = ab^(15t), we need to manipulate the given function.

First, we can rewrite e^(0.12t) as (e^0.12)^t. Since e^0.12 is a constant, let's call it b.

So, b = e^0.12 = 1.1275 (rounded to four decimal places).

Now, let's rewrite f(t) using the new variable b:

f(t) = 30000 * (1.1275)^t

Comparing this with the desired form f(t) = ab^(15t), we can see that a = 30000 and b = 1.1275.

Therefore, the exponential function f(t) = 30000e^(0.12t) can be written in the form f(t) = 30000 * (1.1275)^(15t), rounded to four decimal places.