Podcast
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?
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?
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?
Signup and view all the answers
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?
Signup and view all the answers
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.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
Description
Test your knowledge on the properties of exponential functions with this quick check quiz. You will graph the function y = 5 (1/2)^x + 4 and determine the correct representation. Expand your understanding of exponential behavior and transformations.
