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Q1:
Write an exponential equation in the form π¦ = π ο for the numbers in the table.
Q2:
Write an exponential equation in the form π¦ = π ( π ) ο for the numbers in the table.
Q3:
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.
Q4:
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.
Q5:
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.
Q6:
Write an equation in the form π¦ = π ( π ) ο for the numbers in the table.
Q7:
Q8:
Q9:
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₯ = 1 .
Find the equation that describes the graph in the form π¦ = π π π₯ Ξ π₯ .
Q10:
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 ?
Q11:
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 .
Q12:
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 .
Q13:
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₯ ?
Q14:
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?
Q15:
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.
Q16:
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 .
Q17:
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.
Q18:
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.
Q19:
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.
Q20:
Q21:
Q22:
Write an equation to represent the statement βThe value of π¦ is equal to five to the power of π₯ .β
Q23:
Q24:
Q25:
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
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