Math Problem Statement

The population of a small town is modeled by the exponential function P(t)=3575(1.036)t, where t is the number of years after July 1, 2020. What is the town's percent growth rate? Only the enter the number, as a percent.

Solution

The growth factor in the exponential model is 1.036, which corresponds to a 3.6% growth rate.

The answer is 3.6.

Would you like details on how this was calculated, or do you have any questions?

Here are 5 related questions you might find interesting:

  1. How would the population change after 10 years according to this model?
  2. What is the formula for the population after 5 years?
  3. How does the exponential model compare to a linear growth model for population?
  4. What would happen to the population growth if the rate was 5% instead of 3.6%?
  5. Can the growth factor ever be less than 1? What would that imply?

Tip: Exponential growth models are useful for populations, investments, and anything that grows by a constant percentage over time!

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Math Problem Analysis

Mathematical Concepts

Exponential Growth
Population Modeling

Formulas

P(t) = P_0 * (1 + r)^t
Growth Factor = 1 + r

Theorems

Exponential Growth Theorem

Suitable Grade Level

Grades 9-12

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