5.1 Practice

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical expression that describes a quantity increasing at a constant percentage rate over time, typically represented as y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Front

Write the exponential growth function for a painting worth $1400 increasing by 9% each year.

Back

y = 1400(1.09)^x

Front

What does it mean if a model is classified as exponential decay?

Back

Exponential decay refers to a process where a quantity decreases at a consistent percentage rate over time, typically represented as y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Front

Classify the model A = 1200(0.85)^6 as growth or decay.

Back

Decay

Front

How do you calculate the remaining amount of a substance after a certain time with exponential decay?

Back

Use the formula A = a(1 - r)^t, where 'A' is the remaining amount, 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

If an adult takes 400 mg of ibuprofen and it decreases by 29% each hour, how much is left after 6 hours?

Back

51 mg

Front

What is the formula to calculate the future value of an investment with exponential growth?

Back

The formula is A = P(1 + r)^t, where 'A' is the amount of money accumulated after n years, including interest, 'P' is the principal amount (the initial amount of money), 'r' is the annual interest rate (decimal), and 't' is the time the money is invested for in years.

Front

Calculate the value of a home purchased for $160,000 that increases by 5% per year over 20 years.

Back

$424,527.63

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 over time.

Front

Write the exponential growth function for a model A = 10(1.01)^3.

Back

Growth