Exponential Word Problems Review

Front

What is an exponential growth function?

Back

An exponential growth function is a mathematical expression in the form y = a(b^x), where a is the initial amount, b is the growth factor (b > 1), and x is the time period.

Front

What is an exponential decay function?

Back

An exponential decay function is a mathematical expression in the form y = a(b^x), where a is the initial amount, b is the decay factor (0 < b < 1), and x is the time period.

Front

Identify the equation for exponential growth: y=2(0.5)^x, y=0.5(2)^x, y=0.5x-2, y=2x+0.5

Back

y=0.5(2)^x

Front

If a culture of bacteria starts with 5000 cells and dies by 30% each year, what is the equation representing this situation?

Back

y=5000(0.7)^x

Front

What is the percentage of decay in the function f(x) = 200(0.67)^x?

Back

33%

Front

In the function f(x) = 800(0.85)^x, what is the starting term (a)?

Back

800

Front

If land purchased for $30,000 increases by 5% per year, what is its approximate value in 2011?

Back

$361,223

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth (if > 1) or decay (if < 1) factor.

Front

How do you determine the percentage increase from an exponential function?

Back

The percentage increase is calculated as (b - 1) * 100%, where b is the base of the exponential function.

Front

What is the formula for calculating the future value of an investment with exponential growth?

Back

Future Value = Present Value * (1 + r)^t, where r is the rate of growth and t is the time in years.