Which of the following options results in a graph that shows exponential growth?
a) f(x) = 0.4 (0.2) ^x
b) f(x) = 4(0.98)^x
c) f(x) = 0.7(5)^x
d) f(x) = 5(4) ^-x
I think it is c, can you please help?
@ms.sue @reiny
To determine which option represents exponential growth among the given functions, we need to understand the characteristics of exponential functions.
In general, exponential growth occurs when the base of the exponent is greater than 1. This means that as the value of x increases, the function value increases at an accelerating rate.
Let's review each option to see which one meets this criteria:
a) f(x) = 0.4(0.2)^x:
The base of 0.2 is less than 1, so this function does not represent exponential growth.
b) f(x) = 4(0.98)^x:
The base of 0.98 is less than 1, so this function does not represent exponential growth either.
c) f(x) = 0.7(5)^x:
The base of 5 is greater than 1, so this function does represent exponential growth.
d) f(x) = 5(4)^-x:
In this function, the base of 4 is greater than 1. However, with the negative exponent on the base, this represents exponential decay rather than growth.
Therefore, the correct option that represents exponential growth is c) f(x) = 0.7(5)^x.