Problem 7 - Calculus Early Transcendentals

Question

Give two examples of processes that are modeled by exponential growth.

Step-by-Step Solution

Answer

Question: Provide two examples of processes that are modeled by exponential growth. Answer: Two examples of processes modeled by exponential growth are population growth of a species and compound interest in finance. In population growth, the growth rate is constant, and the population increases by a certain factor or percentage with each time period. In compound interest, the total amount of money grows exponentially as both the initial investment and accrued interest earn additional interest with each compounding period.

Step 1: Example 1: Population Growth

In our first example, we can consider population growth of a species. If there are sufficient resources and an environment with no limiting factors, the population of a species will grow exponentially. In this case, the growth rate, which is affected by birth and death rates, is constant, and the population increases by a certain factor or percentage with each time period.

Step 2: Example 2: Compound Interest

Another example that can be modeled by exponential growth is compound interest in finance. When an initial amount of money (called the principal) is invested at a fixed interest rate, the total amount of money will grow exponentially over a certain period, as long as the interest is compounded (i.e., added to the principal). The exponential growth is due to the fact that not only the initial investment, but also the accrued interest, earns additional interest with each compounding period.