Exponential Functions Regents CRQ

1

Zoe deposited $3,000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years.

1

Graph f(x) = x 2 and g(x) = 2 x
on the set of axes provided over the interval

State which function, f(x) or g(x), has a greater value when x = 20.
Justify your reasoning.

1

The breakdown of a sample of a chemical compound
is represented by the function p(t) = 300(0.5) t ,
where p(t) represents the number of milligrams of the
substance and t represents the time, in years.
In the function p(t), explain what 0.5 represents?

1

The breakdown of a sample of a chemical compound
is represented by the function p(t) = 300(0.5) t ,
where p(t) represents the number of milligrams of the
substance and t represents the time, in years.
In the function p(t), explain what 300 represents?

1

Dylan invested $600 in a savings account at a
1.6% annual interest rate. He made no deposits
or withdrawals on the account for 2 years.
The interest was compounded annually.
Find, to the nearest cent , the balance in the account after 2 years.

1

The number of carbon atoms in a fossil is given
by the function y = 5100(0.95) x , where x represents
the number of years since being discovered.

What is the percent change each year?
Explain how you arrived at your answer.

1

The value, v(t), of a car depreciates according
to the function v(t) = P(.85) t , where
P is the purchase price of the car and t is the time,
in years, since the car was purchased. State the
percent that the value of the car decreases
by each year. Justify your answer.

1

Write an exponential equation for the graph shown.

1

Cole has $10 in his savings account.
Option 1 will add $100 to his account each week.

Write a function in terms of x to model Option 1.

1

Cole has $10 in his savings account.
Option 2 will double the amount in his account
at the end of each week.

Write a function in terms of x to model Option 2.

1

Cole has $10 in his savings account.
Option 2 will double the amount in his account
at the end of each week.

Cole wants to have at least $700 in his account
at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to
reach his goal. Justify your answer.

1

A population of rabbits in a lab, p(x),
can be modeled by the function
p(x) = 20(1.014) x , where x represents
the number of days since the population
was first counted.

Explain what 20 and 1.014 represent
in the context of the problem.

1

A population of rabbits in a lab, p(x),
can be modeled by the function
p(x) = 20(1.014) x , where x represents
the number of days since the population
was first counted.

Determine, to the nearest tenth ,
the average rate of change from
day 50 to day 100.

1

Josephine collects old dolls.
She purchases a doll for $450.
Research shows this doll's value
will increase by 2.5% each year.

Write an equation that determines the value, V ,
of the doll t years after purchase.

1

Josephine collects old dolls.
She purchases a doll for $450.
Research shows this doll's value
will increase by 2.5% each year.

Assuming the doll's rate of appreciation
remains the same, will the doll's value be
doubled in 20 years? Justify your reasoning.

1

A car was purchased for $25,000.
Research shows that the car has an
average yearly depreciation rate of 18.5%.

Create a function that will determine the value,
V(t), of the car t years after purchase.

1

A car was purchased for $25,000.
Research shows that the car has an
average yearly depreciation rate of 18.5%.

Determine, to the nearest cent,
how much the car will depreciate
from year 3 to year 4.

1

Ryan and Hope are studying the spread of dandelions.
Ryan discovers that the growth over t weeks can be
defined by the function f(t) = (8) 2t .

Calculate the number of dandelions
that Ryan will have after 5 weeks.

1

Ryan and Hope are studying the spread of dandelions.
Hope finds that the growth function over t weeks
is g(t) = 2t + 3 .

Calculate the number of dandelions
that Hope will have after 5 weeks.

1

Ryan and Hope are studying the spread of dandelions.
Ryan discovers that the growth over t weeks can be
defined by the function f(t) = (8) 2t .
Hope finds that the growth function over t weeks
is g(t) = 2t + 3 .

Based on the growth from both functions,
explain the relationship between f(t) and g(t) .

0

Please upload pictures of your work if you didn't use the space provided.

0

Please upload pictures of your work if you didn't use the space provided.

0

Please upload pictures of your work if you didn't use the space provided.

0

Please upload pictures of your work if you didn't use the space provided.

0

Zoe deposited $3,000 in an account in the Merrick National Bank, earning 4.2% interest, compounded annually. She made no deposits or withdrawals. Write an equation that can be used to find B, her account balance after t years.

Graph f(x) = x 2 and g(x) = 2 xon the set of axes provided over the intervalState which function, f(x) or g(x), has a greater value when x = 20.Justify your reasoning.

The breakdown of a sample of a chemical compoundis represented by the function p(t) = 300(0.5) t ,where p(t) represents the number of milligrams of thesubstance and t represents the time, in years.In the function p(t), explain what 0.5 represents?

The breakdown of a sample of a chemical compoundis represented by the function p(t) = 300(0.5) t ,where p(t) represents the number of milligrams of thesubstance and t represents the time, in years.In the function p(t), explain what 300 represents?

Dylan invested $600 in a savings account at a1.6% annual interest rate. He made no depositsor withdrawals on the account for 2 years.The interest was compounded annually. Find, to the nearest cent , the balance in the account after 2 years.

The number of carbon atoms in a fossil is givenby the function y = 5100(0.95) x , where x representsthe number of years since being discovered.What is the percent change each year?Explain how you arrived at your answer.

The value, v(t), of a car depreciates accordingto the function v(t) = P(.85) t , whereP is the purchase price of the car and t is the time,in years, since the car was purchased. State thepercent that the value of the car decreasesby each year. Justify your answer.

Write an exponential equation for the graph shown.

Cole has $10 in his savings account.Option 1 will add $100 to his account each week.Write a function in terms of x to model Option 1.

Cole has $10 in his savings account.Option 2 will double the amount in his accountat the end of each week.Write a function in terms of x to model Option 2.

Cole has $10 in his savings account.Option 2 will double the amount in his accountat the end of each week.Cole wants to have at least $700 in his accountat the end of 7 weeks to buy a mountain bike.Determine which option(s) will enable him toreach his goal. Justify your answer.

A population of rabbits in a lab, p(x),can be modeled by the functionp(x) = 20(1.014) x , where x representsthe number of days since the populationwas first counted.Explain what 20 and 1.014 representin the context of the problem.

A population of rabbits in a lab, p(x),can be modeled by the functionp(x) = 20(1.014) x , where x representsthe number of days since the populationwas first counted.Determine, to the nearest tenth ,the average rate of change fromday 50 to day 100.

Josephine collects old dolls.She purchases a doll for $450.Research shows this doll's valuewill increase by 2.5% each year.Write an equation that determines the value, V ,of the doll t years after purchase.

Josephine collects old dolls.She purchases a doll for $450.Research shows this doll's valuewill increase by 2.5% each year.Assuming the doll's rate of appreciationremains the same, will the doll's value bedoubled in 20 years? Justify your reasoning.

A car was purchased for $25,000.Research shows that the car has anaverage yearly depreciation rate of 18.5%.Create a function that will determine the value,V(t), of the car t years after purchase.

A car was purchased for $25,000.Research shows that the car has anaverage yearly depreciation rate of 18.5%.Determine, to the nearest cent,how much the car will depreciatefrom year 3 to year 4.

Ryan and Hope are studying the spread of dandelions.Ryan discovers that the growth over t weeks can bedefined by the function f(t) = (8) 2t .Calculate the number of dandelionsthat Ryan will have after 5 weeks.

Ryan and Hope are studying the spread of dandelions.Hope finds that the growth function over t weeksis g(t) = 2t + 3 .Calculate the number of dandelionsthat Hope will have after 5 weeks.

Ryan and Hope are studying the spread of dandelions.Ryan discovers that the growth over t weeks can bedefined by the function f(t) = (8) 2t .Hope finds that the growth function over t weeksis g(t) = 2t + 3 .Based on the growth from both functions,explain the relationship between f(t) and g(t) .

Please upload pictures of your work if you didn't use the space provided.

Please upload pictures of your work if you didn't use the space provided.

Please upload pictures of your work if you didn't use the space provided.

Please upload pictures of your work if you didn't use the space provided.

Please upload pictures of your work if you didn't use the space provided.

Graph f(x) = x 2 and g(x) = 2 x
on the set of axes provided over the interval

State which function, f(x) or g(x), has a greater value when x = 20.
Justify your reasoning.

The breakdown of a sample of a chemical compound
is represented by the function p(t) = 300(0.5) t ,
where p(t) represents the number of milligrams of the
substance and t represents the time, in years.
In the function p(t), explain what 0.5 represents?

The breakdown of a sample of a chemical compound
is represented by the function p(t) = 300(0.5) t ,
where p(t) represents the number of milligrams of the
substance and t represents the time, in years.
In the function p(t), explain what 300 represents?

Dylan invested $600 in a savings account at a
1.6% annual interest rate. He made no deposits
or withdrawals on the account for 2 years.
The interest was compounded annually.
Find, to the nearest cent , the balance in the account after 2 years.

The number of carbon atoms in a fossil is given
by the function y = 5100(0.95) x , where x represents
the number of years since being discovered.

What is the percent change each year?
Explain how you arrived at your answer.

The value, v(t), of a car depreciates according
to the function v(t) = P(.85) t , where
P is the purchase price of the car and t is the time,
in years, since the car was purchased. State the
percent that the value of the car decreases
by each year. Justify your answer.

Cole has $10 in his savings account.
Option 1 will add $100 to his account each week.

Write a function in terms of x to model Option 1.

Cole has $10 in his savings account.
Option 2 will double the amount in his account
at the end of each week.

Write a function in terms of x to model Option 2.

Cole has $10 in his savings account.
Option 2 will double the amount in his account
at the end of each week.

Cole wants to have at least $700 in his account
at the end of 7 weeks to buy a mountain bike.
Determine which option(s) will enable him to
reach his goal. Justify your answer.

A population of rabbits in a lab, p(x),
can be modeled by the function
p(x) = 20(1.014) x , where x represents
the number of days since the population
was first counted.

Explain what 20 and 1.014 represent
in the context of the problem.

A population of rabbits in a lab, p(x),
can be modeled by the function
p(x) = 20(1.014) x , where x represents
the number of days since the population
was first counted.

Determine, to the nearest tenth ,
the average rate of change from
day 50 to day 100.

Josephine collects old dolls.
She purchases a doll for $450.
Research shows this doll's value
will increase by 2.5% each year.

Write an equation that determines the value, V ,
of the doll t years after purchase.

Josephine collects old dolls.
She purchases a doll for $450.
Research shows this doll's value
will increase by 2.5% each year.

Assuming the doll's rate of appreciation
remains the same, will the doll's value be
doubled in 20 years? Justify your reasoning.

A car was purchased for $25,000.
Research shows that the car has an
average yearly depreciation rate of 18.5%.

Create a function that will determine the value,
V(t), of the car t years after purchase.

A car was purchased for $25,000.
Research shows that the car has an
average yearly depreciation rate of 18.5%.

Determine, to the nearest cent,
how much the car will depreciate
from year 3 to year 4.

Ryan and Hope are studying the spread of dandelions.
Ryan discovers that the growth over t weeks can be
defined by the function f(t) = (8) 2t .

Calculate the number of dandelions
that Ryan will have after 5 weeks.

Ryan and Hope are studying the spread of dandelions.
Hope finds that the growth function over t weeks
is g(t) = 2t + 3 .

Calculate the number of dandelions
that Hope will have after 5 weeks.