Question

The profit a company makes decreases exponentially at a rate of 0.9% per year. In 2014, the profit was $9500. Calculate the profit in 2019.​

Answer 1

Answer: The formula for exponential decay is given by:

P(t) = P0 * e^(-rt)

where P(t) is the profit at time t, P0 is the initial profit, r is the rate of decrease in percentage, and t is the time elapsed in years.

In this case, P0 = $9500, r = 0.9%, and t = 5 (the time elapsed from 2014 to 2019).

First, we need to convert the rate of decrease from a percentage to a decimal:

r = 0.9% / 100 = 0.009

Now, we can plug in the values into the exponential decay formula:

P(5) = $9500 * e^(-0.009 * 5) = $9500 * e^(-0.0455)

We can calculate the value of e^(-0.0455) using a calculator or mathematical software. The result is approximately 0.955.

Therefore, the profit in 2019 is:

P(5) = $9500 * 0.955 = $9027.25

So, the profit in 2019 would be $9027.25.

Explanation: