All exponential functions can be written in many forms. Write the function f, of, t, equals, 13000, left bracket, 1, point, 2, right bracket, start superscript, start fraction, t, divided by, 30, end fraction, end superscriptf(t)=13000(1.2)
30
t
in the form f, of, t, equals, a, e, start superscript, k, t, end superscriptf(t)=ae
kt
. Round all coefficients to four decimal places.
To rewrite the function in the form f(t) = ae^(kt), we need to find the values of a and k.
Given f(t) = 13000(1.2)^((t/30)), we can see that a = 13000 and k = log(1.2)/30.
Using a calculator, we can evaluate k to four decimal places:
k ≈ log(1.2)/30 ≈ 0.0080
Therefore, the function can be written as:
f(t) ≈ 13000 * e^(0.0080t)