Exponential Functions, Half-Life and Compound Interest

Jack invests $4, 886 in a retirement account with a fixed annual interest rate of 6% compounded continuously. What will the account balance be after 13 years?

• $10,658.67

• $12,017.62

• $11,149.27

• $11,317.77

Graph the function f(x) = 5^x and write the domain and range in interval notation.

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After taking a certain antibiotic, the amount of amoxicillin A(t), in milligrams, remaining in the patient's system t hr after taking 1000 mg of amoxicillin is A(t) = 1000e^–0.49t. How much amoxicillin is in the patient's system 3 hours after taking the medication? Round to the nearest tenth of a mg.

• 361.0 mg

• 689.8 mg

• 33.9 mg

• 229.9 mg

What type of function is f(x)=2(1/7)^x ?

• Exponential Growth

• Linear

• Exponential Decay

• None of the Above

Write an exponential function to model the situation. Solve.
The value of a car is $18000 and is depreciating at a rate of 12% per year. What will the value of the car be after 10 years?

• V(t) = 18000(.88)^t ; $12986.98

• V(t) = 18000(.12)^t ; $12986.98

• V(t) = 18000(.88)^t ; $5013.02

• V(t) = 18000(.12)^t ; $5013.02

Write an exponential function to model the situation. Solve.
Bismuth-214 has a half-life of approximately 20 minutes. Find the amount of Bismuth-214 left from a 30-gram sample after 1 hour.

• y = 30 (.5)^t ; 15g

• y = 30 (.5)^t ; 7.5g

• y = 30 (.5)^t ; 3.75g

• y = 30 (.5)^t ; 1.88g

Which function matches the graph?

• f(x) = 1(½)^x - 3

• f(x) = 4(2)^x - 3

• f(x) = 1(2)^x + 3

• f(x) = 4(½)^x - 3

Which function matches the graph?

• f(x) = -5(2)^x + 3

• f(x) = 5(2)^x + 3

• f(x) = 5(2)^x - 3

• f(x) = -5(½)^x + 3

Write an exponential function in the form y=ab^x that goes through points (0,4) and (2,324).

• y=4(9)^x

• y=9(4)^x

• y=2(4)^x

• y=4(81)^x