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ALMultiple Choice

Growth and Decay Factors

Question 1 • Applications and Modeling

Which of the following is false for an exponential growth function y = C(1 + r)t?

Answer
A
when C > 0, the function decreases from left to right
B
the function has a y-intercept of (0, C)
C
the graph of this function will be identical to the graph of y = abx, if a = c and b = 1 + r
D
if C > 0 and r > 0, then the graph will only have positive y-values.

Explanation

When C > 0 and r > 0, the base 1 + r is greater than 1, so y = C(1 + r)^t increases as t increases; it does not decrease from left to right. The other statements are true: setting t = 0 gives y = C, and the function matches y = ab^x when a = C and b = 1 + r. With C > 0 and r > 0, its y-values are also positive.

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