Algebra RC 5

The exponential function f(t) = 500(1.025)^t represents the investment of a $500 at a rate of 2.5% for t years. What would the domain and range be for this function?

• Domain: All real numbers

  Range: All real numbers

• Domain: All real numbers

  Range: y > 500

• Domain: t ≥ 500

  Range: y ≥ 0

• Domain: t ≥ 0

  Range: y ≥ 500

Joey has 7 squash plants. Every month, Joey starts more squash plants so that the number of squash plants he has doubles. After m months he will have S squash plants, where

S = 7(2)^m

How many squash plants will Joey have after 4 months if he keeps all of them and the plants all stay healthy?

• 16

• 56

• 112

• 196

Carrie invested $4,500 at annual interest rate of 5.5%. What does the 5.5% represent in the question?

• Constant rate of change

• Constant ratio of growth

• Initial amount of investment

• Constant ratio of decay

During normal breathing, about 14% of the air in the lungs is replaced after one breath. Which of the following is an exponential decay model for the amount of the original left in the lungs if the initial amount of air in the lungs is 300 mL?

• f(x) = 14(300)^x

• f(x) = 300(14)^x

• f(x) = 300(0.14)^x

• f(x) = 300(0.86)^x

What is the y-intercept of the exponential function?

• (0, 2)

• (0, 15)

• (0, 0)

• (15, 0)

You drink a beverage with 125 mg of caffeine. Each hour, the caffeine in your system decreases by about 14%. What does the 125 mg of caffeine represent in this problem?

• The initial amount of caffeine

• The final amount of caffeine in your body

• The growth ratio of the caffeine in your body

• The decay ratio of the caffeine in your body

Sarah deposited $1,000 into a saving account that compounds annually with an interest rate of 7.5% for 10 years. What is a reasonable range for her total savings account? The formula for compound interest is A = P(1 + r)^t.

• 0 ≤ A ≤ 1000

• 1000 ≤ A ≤ 2070

• 0 ≤ t ≤ 10

• 0 ≤ t ≤ 1000

The table below shows the cooling temperature of a pot of coffee. Using an exponential function to represent the data, when will the pot of coffee be approximately 100 °F?

• 30 minutes

• 45 minutes

• 50 minutes

• 60 minutes

Your new electric car depreciates 6% annually. If you paid $24,500 for your car, what exponential function could be used to represent the depreciation of your car?

• f(x) = 24,500(0.06)^x

• f(x) = 24,500(0.94)^x

• f(x) = 245(0.06)^x

• f(x) = 245(0.94)^x

You received $250 for your birthday and decide to invest it into a savings account that pays you 5%. This function can be modeled by f(x) = 250(1.05)^x. What would you expect for the range of this function?

• y ≥ 250

• y > 250

• x > 0

• x ≥ 0