Question

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.

Answer 1

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.