Exponential Growth and Decay Word Problems

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)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

How do you write an exponential growth function for a value that increases by 9% each year starting from $1400?

Back

y = 1400(1.09)^x, where x is the number of years.

Front

What is the formula to calculate the remaining amount of a substance after a certain percentage decay?

Back

The formula is Q = Q0(1 - r)^t, where Q0 is the initial quantity, 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 1 hour?

Back

Q = 400(1 - 0.29)^1 = 284 mg.

Front

What is the decay rate in the function Q = 3.1(0.78)^t?

Back

The decay rate is 22%, calculated as (1 - 0.78) * 100.

Front

What does the term 'initial quantity' refer to in exponential functions?

Back

The initial quantity is the starting amount before any growth or decay occurs, represented by 'a' in the function y = a(1 + r)^t.

Front

How do you determine the annual growth rate from a population model like P = 6191(1.04)^t?

Back

The annual growth rate is found by subtracting 1 from the growth factor: (1.04 - 1) * 100 = 4%.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a constant percentage rate, while exponential decay occurs when a quantity decreases at a constant percentage rate.

Front

How can you express a decay rate as a percentage?

Back

To express a decay rate as a percentage, subtract the decay factor from 1 and multiply by 100: (1 - decay factor) * 100.

Front

What is the value of Q when t = 0 in the function Q = 3.1(0.78)^t?

Back

Q = 3.1, since any number raised to the power of 0 is 1.