Please Help I don't know what I'm trying to find standard form or simplify

Question

The exponential function  can be written in the standard form . Find the values of  and . Give exact values, not decimal approximations.

Answer 1

Do you mean f(x) = 2(3^2x+5)? If so, then:

f(x) = 2(3^2x)(3⁵) = 486(3^2x) = 486(3²)^x = 486(9)^x

So, A = 486 and b = 9.

Answer 2

I think your equation is:

f(x) = 2·3^2x+5

f(x) = 2·3^2x·3⁵

f(x) = 2·3⁵·(3²)^x

Now 2·3⁵ = 486 and 3² = 9:

f(x) = 486·9^x

which is in the form f(x) = a·b^x where a = 486 and b = 9.