To write the function in the form f(t) = ab(40)^t, we need to rearrange the given function f(t) = 520e^(-0.1t).
First, let's rewrite the expression using the exponent properties for the base e:
f(t) = 520 * e^(-0.1t)
= 520 * (1/e^(0.1t))
Next, we can rewrite the term (1/e^(0.1t)) as (e)^(-0.1t):
f(t) = 520 * (e)^(-0.1t)
Comparing this with the form f(t) = ab(40)^t, we see that:
b = 520
a = e^(-0.1t)
However, in the given problem, we need to round the coefficients to four decimal places. So, let's calculate the value of a for t = 40:
a = e^(-0.1 * 40)
≈ 0.1353
Therefore, the function can be written in the form f(t) = (0.1353)(520)(40)^t, where a ≈ 0.1353 and b = 520.
All exponential functions can be written in many forms. Write the function f, of, t, equals, 520, e, start superscript, minus, 0, point, 1, t, end superscriptf(t)=520e
−0.1t
in the form f, of, t, equals, a, b, start superscript, start fraction, t, divided by, 40, end fraction, end superscriptf(t)=ab
40
t
. Round all coefficients to four decimal places.
1 answer