Question

Is the Growth or Decay Rate for the following

The population in Charlotte can be modeled by the function f(x) = 250,000(1.025)*.
this a growth or decay rate? What is the rate in a percent?
action g(x) = 25.550(0.805)

Answer 1

The function f(x) = 250,000(1.025)^x represents exponential growth with a 2.5% growth rate, while g(x) = 25.550(0.805)^x shows exponential decay with a 19.5% decay rate.

Step-by-step explanation:

The function f(x) = 250,000(1.025)^x models the population in Charlotte, with the base (1.025) being greater than 1.

This indicates exponential growth, as the population increases by a fixed percentage over equal time intervals.

To find the growth rate in percent, we look at the base of the exponential function.

The base 1.025 implies a 2.5% growth rate because 1.025 is equivalent to 100% + 2.5%.

Therefore, each year, the population grows by 2.5%.

In contrast, the function g(x) = 25.550(0.805)^x represents exponential decay because the base (0.805) is less than 1, meaning the quantity is decreasing over time.

The decay rate as a percent is found by subtracting the base from 1 and then multiplying by 100.

Thus, the decay rate is (1 - 0.805) * 100 = 19.5%.

This signifies that the quantity is decreasing by 19.5% each period.