Question

Given the following exponential function, identify whether the change represents growth or decay, and determine the percentage rate of increase or decrease y=330(1.06)^x

Answer 1

Answer: Exponential growth. The growth rate is 6%

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Explanation:

The general form of an exponential function is

y = a*b^x

where 'a' is the initial starting amount and b helps determine if we have exponential decay or exponential growth, and how much of it.

We have a = 330 as the initial amount. Since b = 1.06 is larger than 1, this means we have exponential growth. If 0 < b < 1, then we would have exponential decay.

Solving 1+r = 1.06 leads to r = 0.06 = 6%, showing we have a growth rate of 6%

This means that if we started with say 100 people, and the population grew by 6%, then at the end of the time unit (say 1 year), then we'd have 106 people.