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In this lesson, we will learn how to write equivalent equations for exponential functions using tables of values, graphs, and descriptions.

Q1:

Observe the given graph, and then answer the following questions.

Find the π¦ -intercept in the shown graph.

As this graph represents an exponential function, every π¦ βvalue is multiplied by π when π₯ increases by Ξ π₯ . Find π for Ξ π₯ = 3 .

Find the equation that describes the graph in the form π¦ = π π π₯ Ξ π₯ .

Q2:

Write an equation in the form π¦ = π ( π ) ο for the numbers in the table.

Q3:

As this graph represents an exponential function, every π¦ βvalue is multiplied by π when π₯ increases by Ξ π₯ . Find π for Ξ π₯ = 1 .

Q4:

The number of people who view a meme triples every hour. If 5 friends viewed a meme initially, how many people would have viewed it after one hour?

How many people would have viewed the meme after π‘ hours?

Q5:

What must a number be multiplied by to decrease it by 5%?

Write an equation to represent the statement βTo calculate the value of π¦ , decrease π₯ by 5%.β

A manufacturer aims to decrease the amount of waste they produce by 5% every year. If they currently produce 45 tons of waste, write an equation to calculate π , the amount they aim to produce in π‘ years .

Q6:

Dalia bought an antique vase for $600. The value of the vase increases by 4% each year. Write an equation that can be used to find the value of the vase in dollars, , years after it was purchased.

Q7:

Write an equation to represent the statement βThe value of π¦ is equal to five to the power of π₯ .β

Q8:

The curve below is π¦ = π΄ β π΅ ( 1 β π ) β π₯ for positive constants π΄ , π΅ , and π . Determine these, in that order, using the information in the figure.

Q9:

Write an exponential equation in the form π¦ = π ( π ) ο for the numbers in the table.

Q10:

The producer of a successful radio show predicts that the number of listeners will increase by 0.5% a month. The show currently has 4 5 0 0 0 listeners. Write an equation that can be used to calculate πΏ , the number of listeners they expect to have in π‘ yearsβ time.

Q11:

Write an exponential equation in the form π¦ = π ο for the numbers in the table.

Q12:

Q13:

Q14:

The given graph shows that π¦ = π ( π₯ ) .

Write an explicit formula for π ( π₯ ) in the form π ( π₯ ) = π π ο ο’ .

Graphically estimate the number that π¦ is multiplied by when π₯ increases by 1.

What calculation would allow you to find an accurate value for π if you wanted to write π ( π₯ ) in the form π ( π₯ ) = π π ο ?

Q15:

Write an equation to represent the statement βWhen 1.5 is raised to the power of π₯ and the result is multiplied by 4, the answer is π¦ .β

Q16:

Sherif decided to invest his savings in a high-interest account that pays 7% interest compounded annually. He invests $450 in the account for years and makes no other deposits or withdrawals.

Write an equation that can be used to calculate , the value of his investment in dollars after years.

What will be the value of his investment after 7 years? Give your answer to the nearest dollar.

Sarah invested her savings in the same account 5 years ago. She made no further deposits or withdrawals. If the balance in her account is now , find, to the nearest dollar, her initial deposit.

Q17:

Q18:

Write an equation in the form π¦ = π ο for the numbers in the table.

Q19:

An initial bacteria population π ο¦ doubles every hour, which is described by the formula π = π β 2 ο¦ ο . Write π in the form π = π β π ο¦ ο» ο‘ ο£ stating π in scientific notation, to two significant figures, and find the number by which you would need to multiply the first days population to find the second.

Q20:

Q21:

As this graph represents an exponential function, every π¦ -value is multiplied by π when π₯ increases by Ξ π₯ . Find π for Ξ π₯ = 1 .

Find the equation that describes the graph in the form π¦ = π π ο ο« ο .

Q22:

Write an explicit formula for π ( π₯ ) in the form π ( π₯ ) = π π π₯ 5 .

What calculation would allow you to find an accurate value for π if you wanted to write π ( π₯ ) in the form π ( π₯ ) = π π π₯ ?

Q23:

What must a number be multiplied by to increase it by 13%?

Write an equation to represent the statement βTo calculate the value of π¦ , increase π₯ by 13%.β

A company aims to increase its profits by 13% every year for the next 3 years. If its profit this year is π ο¦ , write an equation to calculate π ο© , the profit in 3 yearsβ time.

Q24:

Q25:

Karim wants to invest his savings. He has found a fund which pays a year, compounded annually. He would like to have in that fund after 3 years. Write an equation that can be used to find , the amount in dollars that Karim must invest for him to have in the fund after 3 years.

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