To write the function f(t)=30000e^(0.12t) in the form f(t)=ab^(15t), we need to rewrite the exponential expression with base e in terms of base 15.
To find the equivalent expression, we first note that e can be written as e = 15^(ln(e)/ln(15)).
Now, let's rewrite the function f(t)=30000e^(0.12t) using this conversion:
f(t) = 30000 * e^(0.12t)
f(t) = 30000 * (15^(ln(e)/ln(15)))^(0.12t)
Using the property of exponents, (a^b)^c = a^(bc):
f(t) = 30000 * 15^((ln(e)/ln(15)) * 0.12t)
Rounding all coefficients to four decimal places, our rewritten function in the form f(t)=ab^(15t) is:
f(t) = 30000 * 15^(0.0578t)
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
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.
1 answer