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In this lesson, we will learn how to set up and solve exponential growth and decay equations and how to interpret their solutions.

Q1:

Is the exponential function π¦ = 4 ( 1 . 2 1 ) π₯ growing or decaying?

Q2:

The population, π , of a city in year π‘ is given by the formula π = 1 0 ( 2 . 6 ) οͺ ο ο± ο¨ ο ο¦ ο¦ ο§ . 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?

Q5:

The value of a car falls by 3 6 % 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 π , in micrograms per liter, of a certain drug in human blood plasma measured at different times. Considering that the concentration after β hours can be modeled with the function π = 1 8 β 0 . 7 5 ο , by what percentage does the drugβs concentration decrease every hour?

Q7:

A carβs value depreciates by π % every year. A new car costs π d o l l a r s .

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

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

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