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Questions and Answers
What is the graph of the function y = 5(1/2)^x + 4?
What is the graph of the function y = 5(1/2)^x + 4?
- Option B
- Option D
- Option C (correct)
- Option A
What is the graph of the function y = 4(1/6)^x + 2?
What is the graph of the function y = 4(1/6)^x + 2?
- Option B
- Option C
- Option D
- Option A (correct)
What is the exponential function that models the decay of a material with a half-life of 42 days, starting with 49 kg? Find the amount remaining after 8 days.
What is the exponential function that models the decay of a material with a half-life of 42 days, starting with 49 kg? Find the amount remaining after 8 days.
y = 49(1/2)^{1/42 x}; 42.940 kg
What is e^1.6 evaluated to the nearest tenth?
What is e^1.6 evaluated to the nearest tenth?
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If you invest $500 at an annual interest rate of 8.2% compounded continuously, how much will you have in the account after 15 years?
If you invest $500 at an annual interest rate of 8.2% compounded continuously, how much will you have in the account after 15 years?
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Study Notes
Exponential Functions and Graphing
- Graph for y = 5(1/2)^x + 4 corresponds to Option C.
- Graph for y = 4(1/6)^x + 2 corresponds to Option A.
Exponential Decay and Half-life
- Half-life of a radioactive material is 42 days.
- Initial mass of the material is 49 kg.
- Exponential decay function: y = 49(1/2)^(1/42)x.
- Remaining mass after 8 days: approximately 42.940 kg.
Evaluating Exponential Functions
- For the function y = e^x, e^1.6 evaluates to approximately 5.0.
Continuous Compounding and Investment Growth
- Investment of $500 at an annual interest rate of 8.2%, compounded continuously.
- Account value after 15 years: approximately $1,710.61.
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