Exponential Growth And Decay Common Core Algebra 1 Homework ~UPD~
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Exponential Growth And Decay Common Core Algebra 1 Homework
In this homework assignment, you will practice solving problems involving exponential growth and decay. Exponential functions are functions that change by a constant percentage rate over equal time intervals. They can be used to model phenomena such as population growth, radioactive decay, compound interest, and more.
Exponential Growth And Decay Common Core Algebra 1 Homework
To solve exponential growth and decay problems, you need to know the following formulas:
For exponential growth, y = a(1 + r), where a is the initial amount, r is the growth rate (as a decimal), and t is the time.
For exponential decay, y = a(1 - r), where a is the initial amount, r is the decay rate (as a decimal), and t is the time.
You can also use the formula y = ab, where a is the initial amount and b is the base of the exponential function. The base b can be found by using the formula b = 1 + r for growth or b = 1 - r for decay.
To complete this homework assignment, you will need to answer 10 questions that involve exponential growth and decay. You will need to show your work and explain your reasoning for each question. You will also need to check your answers using a calculator or an online tool.
The questions are as follows:
A bacteria culture has an initial population of 500 cells and grows by 8% every hour. How many cells will there be after 5 hours?
A radioactive substance has a half-life of 12 years. How much of a 20-gram sample will remain after 36 years?
A car depreciates by 15% every year. If the car was worth $25,000 when it was new, what will it be worth after 4 years?
A bank account earns 3% interest compounded annually. If the initial balance is $10,000, how much money will be in the account after 10 years?
A population of rabbits increases by 20% every month. If there are 50 rabbits at the beginning of January, how many rabbits will there be at the end of March?
A pond has an area of 100 square meters and is covered by water lilies. The water lilies double in area every week. How long will it take for the water lilies to cover the entire pond?
An investment grows by 5% every year. If the initial value is $5,000, how long will it take for the investment to reach $10,000?
A radioactive substance decays by 2% every day. If there are 100 grams of the substance at the beginning of an experiment, how many grams will there be after 10 days?
A culture of yeast grows by 25% every hour. If there are 40 grams of yeast at the start of an experiment, how many grams will there be after 3 hours?
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