Exponential Word Problems

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical expression of the form y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What does the base of an exponential function represent in growth problems?

Back

The base of an exponential function represents the growth factor. If the base is greater than 1, it indicates growth; if it is between 0 and 1, it indicates decay.

Front

How do you determine if an equation represents growth or decay?

Back

If the growth factor (base) is greater than 1, it represents growth. If it is less than 1, it represents decay.

Front

What is the formula to calculate future population given a current population and growth rate?

Back

The formula is P = P0(1 + r)^t, where P0 is the current population, r is the growth rate (as a decimal), and t is the number of years.

Front

If a population increases by 15% each year, what is the growth factor?

Back

The growth factor is 1.15.

Front

Write the exponential growth function for a population of 190,000 increasing by 15% per year.

Back

P(t) = 190000(1.15)^t.

Front

What is the value of an investment of $30,000 growing at 5% per year after 51 years?

Back

The value is approximately $344,022.

Front

How do you convert a percentage increase to a growth factor?

Back

To convert a percentage increase to a growth factor, add 1 to the percentage expressed as a decimal. For example, a 9% increase becomes 1 + 0.09 = 1.09.

Front

What is the equation for a quantity that starts at 5 and increases by 55% each year?

Back

f(t) = 5(1.55)^t.

Front

If a painting's value is $1400 and increases by 9% each year, what is the exponential growth function?

Back

y = 1400(1.09)^x.