Question

Identify whether each function is linear or exponential.

Function A:
Function C
Function D:
You have $200 in
a savings
account that
earns 1% annual
interest
b. Which function has the greatest growth factor? Justify your response.

Answer 1

A)

Function A: Exponential

Function B: Linear

Function C: Exponential

Function D: Exponential

B) Function A

Explanation:

Function A: This is exponential because- (1, 3)(2,9)(3,27)

It is not going up by the same number each time. However, it is multiplying by 3 each time which means it is exponential.

Function B: This is linear because- (1, 64)(1, 80)(1, 96)

It is going up by 16 each time, (a constant number) which means it is linear.

Function C: This is exponential because- there is a curve, linear is always a straight line. But, this has a curve which means it is exponential.

Function D: This is exponential because- It is increasing by a percentage and not a constant number. It is increasing by 1% which means it is exponential.

The function that has the greatest growth factor is Function A because, Function A multiplies by 3 each time. Function B is linear, exponential functions always pass linear functions despite how "steep" they are. Eventually, the exponential function will surpass it. Function C is also exponential but is not as "steep" as Function A. Function A multiplies by 3 each time but Function C increases less. Function D is also exponential, and for the same reasons as Function C, Function A has the greatest growth factor.