Modeling Exponential Functions

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

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

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Use the table to write an exponential function of the form: katex latex="f\left(x\right)=a\cdot b^x"

Use the table to write an exponential function of the form: f\left(x\right)=a\cdot b^x

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The exponential function modeled below represents the number of square kilometers of land occupied by cane toads x years after this animal was first introduced into Australia. Which function best models this data?