Question

The investment of a certain company increases by 20% every year from a starting investment of $500,000. which of the following explicit equations can be used to model how the investment of the company changes with time? the investment of a certain company increases by 20% every year from a starting investment of $500,000. which of the following explicit equations can be used to model how the investment of the company changes with time?

Answer 1

To model the investment increase by 20% annually starting at $500,000, the formula A = 500,000(1 + 0.20)^t is used, where A is the amount after t years, P is the initial investment, r is the annual growth rate, and t is the number of years.

Step-by-step explanation:

To model the investment of a company that increases by 20% every year from an initial amount of $500,000, we use the formula for compound interest. The general form of the equation for compound growth is A = P(1 + r)^t, where:

• A is the amount of money accumulated after n years, including interest.
• P is the principal amount (the initial amount of money before interest).
• r is the annual interest rate (decimal).
• t is the time the money is invested in years.

For this particular scenario, P is $500,000, r is 20% or 0.20, and t represents the number of years. Plugging these into the formula, the explicit equation that models the company's investment over time is:

A = 500,000(1 + 0.20)^t