Which of the following options results in a graph that shows exponential growth
A.f(x)= 0.4(3)^x
B.f(x)= 3(0.5)^x
C.f(x)= 0.8(0.9)^x
D.f(x)= 0.9(5)^-x
A is the only one that has a positive base > 1
so A
To determine which option results in a graph that shows exponential growth, we need to analyze the structure of the functions.
A. f(x) = 0.4(3)^x
The base of the exponential function is 3, and the coefficient is positive. This indicates exponential growth.
B. f(x) = 3(0.5)^x
The base of the exponential function is 0.5, which is less than 1. This indicates exponential decay, not growth.
C. f(x) = 0.8(0.9)^x
The base of the exponential function is 0.9, which is less than 1. This also indicates exponential decay, not growth.
D. f(x) = 0.9(5)^(-x)
The base of the exponential function is 5, and the exponent is negative. This indicates exponential decay, not growth.
Therefore, the only option that results in a graph that shows exponential growth is A. f(x) = 0.4(3)^x.
To determine which of these options results in a graph that shows exponential growth, we need to identify the common characteristics of exponential growth.
Exponential growth occurs when a quantity increases rapidly over time, and it can be represented by the equation f(x) = a * b^x, where a represents the initial amount or starting value, b is the base, and x is the variable representing time.
In this case, let's analyze the given options:
A. f(x) = 0.4(3)^x
B. f(x) = 3(0.5)^x
C. f(x) = 0.8(0.9)^x
D. f(x) = 0.9(5)^-x
We can see that all the options follow the exponential growth form with a constant base raised to the power of x. However, the base values differ for each option.
A. The base is 3.
B. The base is 0.5.
C. The base is 0.9.
D. The base is 5 raised to the power of -x.
By comparing the base values, we can conclude that option D, f(x) = 0.9(5)^-x, does not represent exponential growth because the base is not a positive value. Exponential growth requires a positive base value.
Therefore, the option that results in a graph showing exponential growth is option A, f(x) = 0.4(3)^x, where the base is 3.