All exponential functions can be written in many forms. Write the function f, of, t, equals, 9800, e, start superscript, 0, point, 3, t, end superscriptf(t)=9800e
0.3t
in the form f, of, t, equals, a, b, to the power t f(t)=ab
t
. Round all coefficients to four decimal places.
The exponential function f(t) = 9800e^(0.3t) can be written in the form f(t) = ab^t.
To find the values of a and b, we need to convert the given form into the desired form.
Here's how to do it:
Step 1: Rewrite the given exponential function as f(t) = 9800 * e^(0.3t).
Step 2: Recall that e is Euler's number, which is approximately equal to 2.71828.
Step 3: Substitute the value of e into the equation, giving f(t) = 9800 * (2.71828)^(0.3t).
Now, we can see that a is 9800 and b is approximately equal to 2.71828^(0.3).
Let's calculate the value of b to four decimal places:
b ≈ 2.71828^(0.3) ≈ 1.3499
So, the function f(t) = 9800e^(0.3t) can be written as f(t) = 9800 * (1.3499)^t.