CA^x if f(-2)=8,if f(5)=3

Answer 1

So if that is indeed the exponential function, then

3 = C*a^5 and 8 = C*a^(-2) = C/a^2

3 = C * a^5 and 8*a^2 = C

subsitiuting:

3 = (8*a^2)*a^5

3 = 8 * a^7

3/8 = a^7

a = root7(3/8) = root7(3) * root7(8^6) / 8

C = 8*a^2 = 8 * root7(3/8)^2 = 8 * (3/8)^(2/7)

The exponential function is then y = f(x) = (3/8)^(1/7)^x * 8 * (3/8)^(2/7) =

= (3/8)^(x/7) * 8 * (3/8)^(2/7) =

= 8* (3/8)^{(x+2)/7}