Algebraic Modeling worksheets
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Rhonda deposited $3000 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.
B(t) = 3000(1 - 4.2)t
B(t) = 3000(1 + 4.2)t
B(t) = 3000(1 - 0.042)t
B(t) = 3000(1 + 0.042)t
Marilyn 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.
V(t) = (1 + 0.025)t
V(t) = (1 - 0.025)t
V(t) = (1 + 2.5)t
V(t) = (1 - 2.5)t
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.
V(t) = 25000(1 - 0.185)t
V(t) = 25000(1 + 0.185)t
V(t) = 25000(1 - 18.5)t
V(t) = 25000(1 + 18.5)t
John invested $900 in a savings account at a 2.3% annual interest rate. He made no deposits or withdrawals on the account. Write a function J(t) to represent the amount of money in the account after t years.
J(t) = 900(1 - 0.23)t
J(t) = 900(1 + 0.23)t
J(t) = 900(1 + 0.023)t
J(t) = 900(1 - 0.023)t
The rabbit population started at 65,000 rabbits. The population is decreasing at a rate of 1.5% each year. Write a function r(t) to represent the rabbit population after t years.
r(t) = 65000(1 - 0.015)t
r(t) = 65000(1 + 0.015)t
r(t) = 65000(1 - 1.5)t
r(t) = 65000(1 + 1.5)t
HINT: Use your y= on the calculator to determine which one is equivalent.
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What is the y-intercept of the function: f\left(x\right)=2\left(4\right)^x ?
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\left(4\right)^x
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What is the Growth/Decay factor of the function: f\left(x\right)=2\left(4\right)^x ?
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What represents Growth/Decay on f(x)=a⋅bx ?
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What is the initial value of f(x)= a⋅bx
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Write the equation of the exponential function for the given table.
HINT: STAT EDIT STAT --> CALC #0
y=3^x
y=12\left(3\right)^x
y=3\left(4\right)^x
y=4\left(3\right)^x
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B
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The bear population in a given area is currently 1580. They anticipate the bear population to decrease by 2% each year. Which function represents the population of bears, B, after t years.
B = 1580(0.02)t
B = 1580(1 – 0.02)t
B = 1580(1 + 0.02)t
B = 1580(1 – 0.2)t
The population of a town is currently 6342 and is increasing by a rate of 1.3% each year. Which function represents the population of people, P, after t years.
P = 6342(1 + 1.3)t
P = 6342(1 – 1.3)t
P = 6342(1 + .013)t
P = 6342(1 – .013)t
Which of the following functions shows an initial amount of $15 and an increase of 35% each year?
y = 15(1.035)x
y = 15(1.35)x
y = 15(0.35)x
y = 15(0.65)x
is it a growth factor or a decay factor?
Growth Factor
Decay Factor
What is the equation of the following table?
HINT: Use your STAT Key on your calculator
y = 7(2)x
y = 4x + 7
What is the equation of the following table?
HINT: Use your STAT Key on your calculator
y = 2x + 4
y = 4(2)x
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