Gr 11 Math Ch 1: Math Applications of Exponentials
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Gr 11 Math Ch 1: Math Applications of Exponentials

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Questions and Answers

What is the primary purpose of using exponential models?

To model real-world phenomena such as population growth and radioactive decay

What does the formula P(t) = P_0 (1 + r)^t represent?

The formula for exponential growth or decay

What is the first step in solving an exponential problem?

Identify the variables

What is the growth rate in an exponential decay model?

<p>Negative</p> Signup and view all the answers

What is the purpose of converting percentage rates to decimal form?

<p>To ensure the formula is used correctly</p> Signup and view all the answers

Which set of numbers includes all rational and irrational numbers?

<p>( \mathbb{R} )</p> Signup and view all the answers

What is the formula for compound interest similar to?

<p>The formula for exponential growth</p> Signup and view all the answers

What is the purpose of using exponential models in finance?

<p>To calculate the amount of money accumulated over time with a given interest rate</p> Signup and view all the answers

In an exponential growth model, what happens to the quantity each period?

<p>It increases by a fixed percentage.</p> Signup and view all the answers

What does the variable P_0 represent in the exponential growth or decay formula?

<p>The initial amount.</p> Signup and view all the answers

What is the purpose of converting percentage rates to decimal form in exponential problems?

<p>To ensure the formula is used correctly.</p> Signup and view all the answers

Which set of numbers includes natural numbers, whole numbers, integers, rational numbers, and irrational numbers?

<p>R</p> Signup and view all the answers

What is the difference between an exponential growth model and an exponential decay model?

<p>The growth rate is positive in growth and negative in decay.</p> Signup and view all the answers

What is the formula for exponential growth or decay used for in finance?

<p>To calculate the amount of money accumulated over time with a given interest rate.</p> Signup and view all the answers

What is the result of applying the exponential growth or decay formula?

<p>The final amount after time t.</p> Signup and view all the answers

What is the first step in solving a population growth problem?

<p>Identify the variables.</p> Signup and view all the answers

If a population grows from 1000 to 1200 in 2 years, what is the annual growth rate?

<p>5%</p> Signup and view all the answers

A savings account earns an annual interest rate of 4%. If the initial deposit is $500, how much will it be worth after 5 years?

<p>$650</p> Signup and view all the answers

A radioactive substance has a half-life of 10 years. If the initial amount is 100 grams, what will be the amount after 20 years?

<p>25 grams</p> Signup and view all the answers

What is the difference between the exponential growth and decay formulas?

<p>The exponent is positive for growth and negative for decay</p> Signup and view all the answers

A company's sales are expected to grow at an annual rate of 8%. If the current sales are $1 million, what will be the sales in 3 years?

<p>$1,260,000</p> Signup and view all the answers

A bacteria culture grows at a rate of 20% per hour. If the initial population is 1000, what will be the population after 5 hours?

<p>3200</p> Signup and view all the answers

What is the relationship between the exponential growth and decay formulas?

<p>They are equivalent, but with different signs</p> Signup and view all the answers

If a population decreases from 5000 to 3000 in 5 years, what is the annual decay rate?

<p>10%</p> Signup and view all the answers

What is the primary difference between exponential growth and decay models?

<p>The growth rate is positive in growth models and negative in decay models.</p> Signup and view all the answers

If a population grows at a rate of 5% per year, what is the growth factor after 2 years?

<p>1.05^2</p> Signup and view all the answers

What is the purpose of the exponential growth formula in finance?

<p>To calculate the amount of money accumulated over time with a given interest rate.</p> Signup and view all the answers

A population grows from 2000 to 2400 in 2 years. What is the annual growth rate?

<p>5%</p> Signup and view all the answers

What is the difference between a natural number and a whole number?

<p>A natural number is a subset of whole numbers.</p> Signup and view all the answers

What is the result of applying the exponential growth or decay formula?

<p>The final amount after a certain time period.</p> Signup and view all the answers

What is the relationship between the growth rate and the time period in an exponential growth model?

<p>The growth rate is independent of the time period.</p> Signup and view all the answers

A radioactive substance decays at a rate of 20% per year. If the initial amount is 500 grams, what is the amount after 3 years?

<p>160 grams</p> Signup and view all the answers

What does the variable r represent in the exponential growth or decay formula?

<p>The growth rate</p> Signup and view all the answers

Which of the following is an example of exponential decay?

<p>Radioactive decay</p> Signup and view all the answers

What is the formula for exponential growth or decay used for in population growth?

<p>To predict the future population</p> Signup and view all the answers

What is the purpose of converting percentage rates to decimal form in exponential problems?

<p>To ensure accurate calculations</p> Signup and view all the answers

Which set of numbers includes all rational and irrational numbers?

<p>Real numbers</p> Signup and view all the answers

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