Question

Which of these values for Pand a will cause the function f(x)=Pa to be an exponential growth function?

A. P= 5; a = 1)
B. P= a; a=2
C. P = };
D. P= 5; a = 1

Answer 1

For f(x)=P*ax to be an exponential growth function, the base a must be greater than 1. Therefore, the correct values that will result in exponential growth are B. P= a; a=2.

Step-by-step explanation:

To determine which values for P and a will cause the function f(x)=P*ax to be an exponential growth function, we need to identify the conditions that result in growth rather than decay. For an exponential function to represent growth, the base of the exponent (a) must be greater than 1. Looking at the options given:

• A. P= 5; a = 1 does not show growth as a is equal to 1, which represents no change, not growth.
• B. P= a; a=2 does represent exponential growth because a is greater than 1.
• C. P = 1/a; a=1/2 does not show growth; in fact, it shows decay as a is less than 1.
• D. P= 5; a = 1 is identical to option A and does not represent growth.

Therefore, the correct answer is B. P= a; a=2, which will cause the function to be an exponential growth function.