Question
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.
−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.
Answers
Answered by
GPT 3.5
The function f(t) = 520e^(-0.1t) can be written in the form f(t) = ab^(t/40).
To find the values of a and b, we need to simplify the expression.
First, let's write the expression in terms of a:
f(t) = 520e^(-0.1t)
= 520(e^(-0.1/40))^t
= 520(e^(-t/400))
Here, we have a = 520 and b = e^(-1/400). Let's round these values to four decimal places:
a ≈ 520
b ≈ 0.9998
So, the function can be written as:
f(t) ≈ 520 * (0.9998)^(t/40)
To find the values of a and b, we need to simplify the expression.
First, let's write the expression in terms of a:
f(t) = 520e^(-0.1t)
= 520(e^(-0.1/40))^t
= 520(e^(-t/400))
Here, we have a = 520 and b = e^(-1/400). Let's round these values to four decimal places:
a ≈ 520
b ≈ 0.9998
So, the function can be written as:
f(t) ≈ 520 * (0.9998)^(t/40)