Question

Determine whether each function is an example of exponential growth or decay. then find the y-intercept y=2(4)^x

Answer 1

The exponential function in its generic form is given by:
 y = A (b) ^ x
 Where,
 A: initial amount
 b: growth / decrease rate (b <1: decrease, b> 1: growth).
 We have the following function:
 y = 2 (4) ^ x
 We observed that:
 b = 4> 1
 Therefore, the function is an example of exponential growth.
 We look for the intersection with the y axis. For this, we evaluate the function for x = 0:
 y = 2 (4) ^ 0
 y = (2) * (1)
 y = 2
 Answer:
 The function is an example of exponential growth.the y-intercept is:
 y = 2