Exponential Functions Quiz

Mr. Cho purchased a CD with an annual interest rate of 4% in 2017, deposited it for 3 years, and in 2020, he extended it under the same interest rate for 5 years until 2025. Which statement describes this situation to calculate the total percent increase in his principal money from 2017 to 2025?

• 1.048 is multiplied to principal because 1.0431.045=1.048

• 1.048 is multiplied to principal because 1.043+1.045=1.048

• 1.0415 is multiplied to principal because 1.0435=1.0415

• 1.0415 is multiplied to principal because 1.0431.045=1.0415

Mr. Cho is looking to buy a used car that was manufactured one year ago. While doing automobile research, he saw the following advertisement today. Year made Current Value Annual Depreciation rate 2024 (1 year old) $26,912.75 17% Express the value of this car as an exponential function. Explain how each number was calculated.

The number of viruses in the lab increases every hour at the rate shown in the table below. Find the equation to describe this increasing pattern and calculate how many hours are taken to reach 2000 viruses (round to nearest tenth.)

There are two bank accounts with the following conditions: Bank A: 2.5% annual interest compound monthly Bank B: 2.5% annual interest compound quarterly Mr. Cho wants to invest $3,500 today. After 5 years, which bank will give him more money? How much is it?

A population of indigenous people on an island are suffering from a terrible, terrible epidemic. It kills 30% of the population each month. If the starting population is 4,000, how many will be left after 6 months?

• 400 people

• 470 people

• 510 people

• 670 people

A house purchased for $300,000 in 2010 (15 years ago) has increased its value by 1.5% per year. Choose the correct expression for the value in t years later (t years after 2025). Select all that apply.

• f(t) =300000(1.015)15+t : True (Total time is added to exponent.)

• ft =300000[(1.015)15+(1.015)t] False (Growth factors are multiplied to get the total amount, not added.)

• f(t) =300000[(1.015)15(1.015)t] True (Addition of exponent is equivalent to multiplication of exponents with same bases.)

• f(t) =300000(1.15)15+t : False (% was miscalculated. 1.5 must be 0.015)

• f(t) =3000001.01515t False (You are supposed to put power only on growth factor,)

A car was purchased for $30,000. After purchase, the market value of the car is estimated by the expression: f(t) =30000(0.9)t, t years after its purchase. What is the meaning of the expression f(t) =30000(0.9)t?

• Every year, the value of the car is estimated to be down by 9% from the previous year’s value.

• Every year, the value of the car is estimated to be down by 90% from the previous year’s value.

• Every year, the value of the car is estimated to be down by 1% from the previous year’s value.

• Every year, the value of the car is estimated to be down by 10% from the previous year’s value.

The value of an antique worth $2000 in 2025 will increase by 3.5% per year. What is the value of this antique in 2034?

Uranium-235 (U-235) is a radioactive isotope of uranium with a half-life of 703.8 million years, and its remaining amount is expressed as the equation f(t) = P(0.5)t/703.8, where P is the initial amount of uranium and t is the number of years. How many years does it take for 200g of Uranium-235 to be reduced to 50g without any addition or subtraction? (round to the nearest whole number)

Find the equivalent expression for (5)x(5)3x ? Select all that apply.

• (5)1/3 False (Division of same bases is subtraction of the exponents, not division.)

• (5)x - 3x True (Division of same bases is subtraction of the exponents.)

• -5x : False (Negative exponent is converted to its positive exponent with the reciprocal base, not negative base.)

• 1(5)x : True (Negative exponent is converted to its positive exponent with the reciprocal base.)

• (5)-x : True (Division of same bases is subtraction of the exponents.)