Without graphing, determine whether the function represents exponential growth or exponential decay. Then find the y-intercept.
f(x) = 5(4)^x
The given function is f(x) = 5(4)^x.
To determine whether the function represents exponential growth or exponential decay, we need to look at the base of the exponential term, which is 4 in this case.
If the base is greater than 1, then the function represents exponential growth. If the base is between 0 and 1 (exclusive), then the function represents exponential decay.
In this case, the base is 4, which is greater than 1. Therefore, the function represents exponential growth.
To find the y-intercept, we can plug in x = 0 into the function.
f(0) = 5(4)^0 = 5(1) = 5.
So, the y-intercept of the function is 5.