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Solving Investment and Population Growth Problems with Mathematical Models

This document explores various problems in finance and biology through the application of logarithmic and exponential functions. We derive formulas for investment growth and analyze the decay of a substance through half-life calculations. Additionally, we investigate the population growth of guppies in a limited tank environment. Specifically, we calculate when a $1500 investment grows to $2280 at a 7% APR compounded monthly, determine the time for a 3.5g substance to decay to 1 gram, and model guppy population dynamics. The aim is to provide clear solutions for these real-world applications.

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Solving Investment and Population Growth Problems with Mathematical Models

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  1. Solving application problems using logs…

  2. Solve for t: S = P(1+r)t

  3. Solve for n: A = Pe(r●n)

  4. Determine when an investment of $1500 accumulates to a value of $2280 if the investment earns interest at a rate of 7%APR compounded monthly.

  5. The half-life of a certain substance is 65 days and there are 3.5grams present initially. When will there be 1 gram left?

  6. $12,000 is invested into an account that earns 2.25% APR compounded continuously. How long before there is $15,000 in the account?

  7. Solve for x.

  8. A 2000-gallon tank can support no more than 150 guppies. Six guppies are introduced into the tank. After 2.5 weeks 138 guppies are present. a) Write a model for the population in the form: b) How long will it take for the guppy population to be 125?

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