In this worksheet, we will practice setting up and solving exponential growth and decay equations and interpreting their solutions.

**Q2: **

The population, , of a city in year is given by the formula . Determine the year in which the population of the city was 8 million.

**Q3: **

Bassem invests in a savings account. After ten years, the value of his investment had doubled. What was the annual rate of interest? Give your answer to one decimal place.

**Q4: **

A population of bacteria in a petri dish hours after the culture has started is given by . Sarah says this means that the growth rate is per hour. Her friend Engy, however, says that the hourly growth rate is . Who is right?

- AEngy
- BSarah

**Q5: **

The value of a car falls by over 2 years. By considering a suitable exponential function, find the equivalent annual rate of depreciation that would produce the same fall in value over two years.

**Q6: **

The given figure shows the concentration , in micrograms per liter, of a certain drug in human blood plasma measured at different times. Considering that the concentration after hours can be modeled with the function , by what percentage does the drugβs concentration decrease every hour?

- A
- B
- C
- D
- E

**Q7: **

A carβs value depreciates by every year. A new car costs .

Write a function that can be used to calculate , the carβs value in dollars, after years.

- A
- B
- C
- D
- E

What is the value of for which the carβs value will be halved in 3 years? Give your answer to the nearest whole number.