Exponential Growth and Decay Problems

Questions and Answers

Find a bank account balance if the account starts with $100, has an annual rate of 4%, and the money is left in the account for 12 years.

160.10

How much caffeine will you have left in your system after drinking a beverage with 120 mg of caffeine, where the caffeine decreases by about 13% each hour for 4 hours?

68.74

How many players remain after 5 rounds if the tournament starts with 128 participants and half of the players are eliminated during each round?

How many cell phone subscribers were there in 1994 if there were 285 subscribers in 1985 and the number increases by 75% per year?

43872 Signup and view all the answers

How much of the original air is present after 240 breaths if during normal breathing about 12% of the air in the lungs is replaced after each breath and the initial amount of air is 500 mL?

2.37e-11 Signup and view all the answers

Simplify: $24x^6y^{-3} / (12x^{-8} y^7)$

2x^14 y^4 Signup and view all the answers

Simplify: $-(9xy)^0$

-1 Signup and view all the answers

Simplify: $5x^2y (2x^4 y^{-3})$

10x^6 / y^2 Signup and view all the answers

How long would it take to double your principal at an annual interest rate of 7% compounded continuously?

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If you invest $2000 at an annual interest of 5.5% compounded continuously, how much will you have in the account in 10 years?

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What is the value of a painting in 25 years if the original value is $1400 and it increases by 9% each year?

$12,072.31 Signup and view all the answers

What is the value of a sculpture in 2006 if its value in 2000 was $1200 and it is increasing at a rate of 8% per year?

$1904.25 Signup and view all the answers

How many people will remain in the population of a town in 2008 if the population is decreasing at a rate of 1% per year from 1300 people in 2000?

1200 people Signup and view all the answers

What is the fish population after 7 years if it originally was 48,000 and is decreasing at a rate of 3% per year?

38,783 fish Signup and view all the answers

Study Notes

Bank Account Growth

Starting balance of $100 with a 4% annual interest rate over 12 years results in a balance of $160.10.

Caffeine Decay

Consuming 120 mg of caffeine decreases by 13% each hour; after 4 hours, approximately 68.74 mg remains in the system.

Tennis Tournament Elimination

A tournament begins with 128 participants; after 5 rounds of halving, only 4 players remain.

Cell Phone Subscribers

In 1985, there were 285 cell phone subscribers, growing at 75% annually; by 1994, subscribers increased to 43,872.

Lung Air Replacement

Initial lung capacity of 500 mL, with a 12% air replacement each breath leads to approximately 2.37e-11 mL remaining after 240 breaths.

Algebraic Simplification

Simplifying ( \frac{24x^6y^{-3}}{12x^{-8}y^7} ) results in ( 2x^{14}y^{4} ).
Simplifying ( -(9xy)^0 ) results in -1.
Simplifying ( 5x^2y(2x^4y^{-3}) ) results in ( \frac{10x^6}{y^2} ).

Continuous Compound Interest

Time to double principal with a 7% annual rate compounded continuously is part of a hypothetical question without a specific answer provided.

Investment Growth

Investing $2000 at a 5.5% annual interest rate compounded continuously:
- After 10 years, exact future value not calculated.
- Duration needed to grow to $5000 is explored without a specific answer.

Artwork Value Increase

A painting valued at $1400 increasing by 9% annually will be worth approximately $12,072.31 in 25 years.

Sculpture Valuation

A sculpture valued at $1200 in 2000, increasing at 8% per year, will reach a value of approximately $1,904.25 in 2006.

Population Decay

A town with a population of 1300 in 2000 decreasing at a rate of 1% annually will have about 1200 residents by 2008.

Fish Population Decline

An original fish population of 48,000 decreasing at 3% per year results in an estimated population of 38,783 after 7 years.

Description

This quiz covers various word problems related to exponential growth and decay. You'll solve scenarios involving bank account balances and caffeine reduction over time. Test your understanding of these fundamental concepts in mathematics!