5.4 Exponential Applications Lesson Check

Front

What is exponential decay?

Back

Exponential decay refers to a decrease in quantity at a rate proportional to its current value, often represented by the formula A = Pe^(-rt), where A is the amount remaining, P is the initial amount, r is the decay rate, and t is time.

Front

What is the formula for continuous compound interest?

Back

The formula for continuous compound interest is A = Pe^(rt), where A is the amount of money accumulated after time t, P is the principal amount, r is the annual interest rate, and t is the time in years.

Front

How do you identify if a function represents growth or decay?

Back

If the base of the exponential function f(x) = a(b)^x is greater than 1, it represents growth. If the base is between 0 and 1, it represents decay.

Front

What does the b-value in an exponential function indicate?

Back

The b-value (common ratio) indicates the rate of growth or decay. If b > 1, it indicates growth; if 0 < b < 1, it indicates decay.

Front

Calculate the population after 10 years if a population of 1500 decreases by 1.5% per year.

Back

After 10 years, the population will be approximately 1290 deer.

Front

What is the rate of decay in the function f(x) = 5000(0.7)^x?

Back

The rate of decay is 30%.

Front

What is the difference between exponential growth and linear growth?

Back

Exponential growth increases at a rate proportional to its current value, leading to faster increases over time, while linear growth increases by a constant amount.

Front

What is the significance of the number 'e' in exponential functions?

Back

The number 'e' (approximately 2.718) is the base of natural logarithms and is used in continuous growth or decay models.

Front

What is the formula for calculating the future value of an investment compounded monthly?

Back

The formula is A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years.

Front

What does it mean if a population is decreasing by 1.5% per year?

Back

It means that each year, the population is reduced by 1.5% of its current size.