Question

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.

Answer 1

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)