Explain how population and money earning interest can both be represented by the formula A = 1000(1.08)^t.
I have no idea how to solve this problem or how to start!
Thank you! :-)
Sure! The formula A = 1000(1.08)^t represents both population growth and earning interest. Let's break it down step by step.
In the formula, A represents the final amount, t represents the time in years, and 1.08 represents the growth or interest rate. The initial amount is 1000.
For population growth:
Imagine you have a population of 1000 and each year it grows by 8%. To calculate the population after a certain number of years, you multiply the initial population (1000) by 1.08 raised to the power of t (the number of years).
For example, if you want to find the population after 5 years, you would calculate A = 1000(1.08)^5.
For earning interest:
Imagine you have $1000 in a bank account that pays an annual interest rate of 8%. To calculate the amount of money in the account after a certain number of years, you multiply the initial amount ($1000) by 1.08 raised to the power of t (the number of years).
For example, if you want to find the amount of money in the account after 5 years, you would calculate A = 1000(1.08)^5.
So, in both cases, the formula A = 1000(1.08)^t can be used to represent the growth of a population or the increase in money due to earning interest over time.
To solve this problem, you simply substitute the value of t with the number of years you want to calculate (e.g., 5 years) and then perform the calculations according to the given formula.