Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease:

y = 46(1.034)^x
A) Growth, 3.4%
B) Decay, 3.4%
C) Growth, 103.4%
D) Decay, 103.4%

Answer 1

The function y = 46(1.034)^x represents exponential growth at a rate of 3.4%, because the base of the exponent, 1.034, is greater than 1.

Step-by-step explanation:

The given exponential function is y = 46(1.034)^x. To identify whether the change represents growth or decay, we look at the base of the exponential part, which is 1.034. Since this number is greater than 1, it suggests that the function represents exponential growth as the value of y increases as x increases.

The percentage rate of increase, in this case, can be determined by subtracting 1 from the base of the exponent and then multiplying by 100 to convert it into a percentage. Therefore, the percentage rate of increase is (1.034 - 1) × 100% = 3.4%. Based on this information, the correct answer is:

A) Growth, 3.4%