Question

The exponential function f, represented in the table, can be written as

f(x) = a.br.
x f(x)
0
15
19
Complete the equation for f(x).
f(x)=[

Answer 1

The exponential function representing the given table is f(x) = 15 * (3/5)^x.

To determine the exponential function f(x) = a * b^x based on the given table, we can substitute the provided values for x and f(x) to solve for the unknown constants a and b. The table provides two data points:

x = 0, f(x) = 15

x = 1, f(x) = 9

Substitute these values into the exponential function:

15 = a * b^0 (since any number raised to the power of 0 is 1)

9 = a * b^1

From the first equation, b^0 = 1, so a = 15.

Substitute a = 15 into the second equation:

9 = 15 * b^1

Now, solve for b:

b = 9/15 = 3/5

Therefore, the exponential function is:

f(x) = 15 * (3/5)^x

In summary, the exponential function f(x) can be expressed as f(x) = 15 * (3/5)^x.