If f is an exponential function of the form f(x)=C times a^x with growth factor 5 and f(5)=14. What is f(6)?

I know f(6) is 70 but how do you set up the equation to get 70?

f(x) grows by 5 when x grows by 1

f(5 = 14
5 * 14 = 70 = f(6)

f(x) = c 5^x
f(5) = 14 = c 5^5 = 3125 c

c = 14/3125

f(x) = (14/3125) 5^x
if x = 6
f(6) = (14/3125)5^6
= (14 /3125) 15625
= 70

Thanks

You are welcome.

To set up the equation, we can start with the given information that f(x) is an exponential function of the form f(x) = C * a^x, where C is a constant and a is the growth factor.

Since we are given that the growth factor is 5, we can rewrite the equation as f(x) = C * 5^x.

To find the value of C, we can use the second piece of information given: f(5) = 14. This means that when x = 5, the value of f(x) is 14.

Substituting these values into the equation, we get:

14 = C * 5^5

Simplifying the equation:

14 = C * 3125

To solve for C, we divide both sides by 3125:

C = 14/3125

Now that we have the value of C, we can substitute it back into the original equation to find f(6):

f(6) = (14/3125) * 5^6

Simplifying:

f(6) = (14/3125) * 15625

f(6) = 70