Which equation represents exponential growth?
a. f(x) = 4(0. 07)^x
b. f(x) = 2(0. 44)^x
c. f(x) = 1/2(6)^x
d. f(x) = 7(1/2)^x
b. f(x) = 2(0.44)^x
I think it is c
Apologies for the confusion. You are correct, c. f(x) = 1/2(6)^x represents exponential growth.
To determine which equation represents exponential growth, we need to look at the form of the equation. In exponential growth, the base of the exponent is greater than 1.
Let's analyze the given options:
a. f(x) = 4(0.07)^x
b. f(x) = 2(0.44)^x
c. f(x) = 1/2(6)^x
d. f(x) = 7(1/2)^x
Looking at option a:
f(x) = 4(0.07)^x
The base of the exponent here is 0.07, which is less than 1. Hence, it does not represent exponential growth.
Looking at option b:
f(x) = 2(0.44)^x
The base of the exponent here is also 0.44, which is less than 1. Therefore, it does not represent exponential growth.
Looking at option c:
f(x) = 1/2(6)^x
The base of the exponent here is 6, which is greater than 1. However, in this equation, the coefficient in front of the base is 1/2. This means that the function decreases as x increases, indicating exponential decay rather than growth.
Looking at option d:
f(x) = 7(1/2)^x
The base of the exponent here is 1/2, which is less than 1. However, the coefficient in front of the base is 7, indicating exponential growth.
Therefore, the equation that represents exponential growth is d. f(x) = 7(1/2)^x.