Which of the following is a function equivalent to f(x) = 5(1.9)^3x?
f(x) = 34.29^x
f(x) = 5(6.86^x)
f(x) = 5(6.86)x
f(x) = 328.51^x

Solution:

Given f(x) = 5(1.9)^3x

We have properties of exponents that (a^m)ⁿ = a^mn

Here, a = 1.9 ; mn = 3x

f(x) = 5((1.9)³)^x

We know 1.9³ = 6.86

f(x) = 5(6.86)^x

Thus f(x) = 5(1.9)^3x is equivalent to f(x) = 5(6.86^x)

Which of the following is a function equivalent to f(x) = 5(1.9)^3x?

Summary:

A function equivalent to f(x) = 5(1.9)^3x is f(x) = 5(6.86^x).