Exponential Growth and Decay Formulas

Which formula would you use for the following problem? If $1,000 is invested at 16% interest, compounded continuously, for five years, what is the ending balance?

What is the formula to represent exponential growth or decay, where 'a' is the amount after time 't', 'r' is the rate of increase or decrease, and 't' is time?

• f(t) = a * r * t

• f(t) = a * r / t

• f(t) = a * r^t

• f(t) = a * (1 + r)^t

If the original value of an investment is $1,800 and it increases by 7% each year, what is the exponential function to model this situation?

• a = 1800 * (1 + 0.07)^t

• a = 1800 * (1 - 0.07)^t

• a = 1800 * (0.07)^t

• a = 1800 / (1 + 0.07)^t

How do exponential growth and decay formulas differ?

• The initial amount differs.

• The rate differs.

• The time differs.

• The distance differs.

What occurs when a quantity exponentially increases over time?

• Exponential Decay

• Exponential Growth

• Linear Growth

• Linear Decay

In 2002, Oakview High School had 972 students enrolled. If the number of students increased by 1.5% each year, what would be the exponential model of the number of students enrolled in 2014?

• 972 * (1 + 0.015)^12

• 972 * (1 - 0.015)^12

• 972 * (1 + 0.015)^2

• 972 / (1 + 0.015)^12

What occurs when a quantity exponentially decreases over time?

• Exponential Growth

• Linear Decay

• Exponential Decay

• Linear Growth

If an investment of $12,000 is losing value at a rate of 4% each year, what is the exponential function to model this situation?

• a = 12000 * (1 - 0.04)^t

• a = 12000 * (1 + 0.04)^t

• a = 12000 * (0.04)^t

• a = 12000 / (1 - 0.04)^t

Mark bought a brand new car for $35,000 in 2008. If the car depreciates in value approximately 8% each year, what is the exponential function to model this situation?

• a = 35000 * (1 - 0.08)^t

• a = 35000 * (1 + 0.08)^t

• a = 35000 * (0.08)^t

• a = 35000 / (1 - 0.08)^t

The equation y = a(1 - r)^x is used for:

• 1/2 life

• Interest

• Exponential Growth

• Exponential Decay