All exponential functions can be written in many forms. Write the function f, of, t, equals, 86000, e, start superscript, minus, 0, point, 1, 9, t, end superscriptf(t)=86000e
−0.19t
in the form f, of, t, equals, a, b, start superscript, start fraction, t, divided by, 11, end fraction, end superscriptf(t)=ab
11
t
. Round all coefficients to four decimal places.
The function can be written as:
f(t) = a * b^ (t/11)
To find the values of a and b, we can compare this form with the given form:
a * b^ (t/11) = 86000 * e^ (-0.19t)
Comparing the coefficients, we have:
a = 86000
b^ (1/11) = e^ (-0.19)
Taking the 11th power of both sides:
b = e^ (-0.19 * 11)
Now we can substitute the values of a and b into the function:
f(t) = 86000 * (e^ (-0.19 * 11))^ (t/11)
Rounding to four decimal places:
f(t) = 86000 * (0.5026)^ (t/11)