Exponential Growth or Decay Given Equations

Does the following equation model growth or decay? y = 500(.30)^x + 7

• Growth by 30%

• Growth by 70%

• Decay by 30%

• Decay by 70%

Use the function, N = 14,000(.96)^t. Where N is the number of employees and t is the number of years.
How many employees will there be after 3 years?

• 14,000 employees

• 12,386 employees

• 40,360 employees

• 15,748 employees

Determine if the graph represents growth or decay. Also determine the y-intercept.

• decay, 5

• decay, 1

• growth, 5

• growth, 1

What values of b make an exponential growth function?

• b > 1

• 0 < b < 1

Answer explanation

A multiplier that is larger than 1 causes y-values to increase (exponential growth).

What values of b make an exponential decay function?

• b > 1

• 0 < b < 1

Answer explanation

A multiplier that is larger than 0 (positive) but less than 1 causes y-values to decrease (exponential decay).

Does this graph represent exponential growth or decay?

• Growth 

• Decay

• Cannot Be Determined

Answer explanation

The graph is decreasing, so this is exponential decay. The multiplier must be larger than 0, but less than 1

0 < b < 1

A substance starts with a mass of 310 grams and decays at 8.9% per hour. Write an equation to model the situation.

Answer explanation

The initial mass is 310 grams, so a = 310. Find the mulitplier:

100% - 8.9% = 91.1%

Covert this percent to a rate by dividing by 100.

91.1/100 = 0.911

So, b = 0.911

Write the equation of the exponential function.

Answer explanation

The y-intercept is (0,2), so a = 2.

Find b by dividing a y-value by the previous y-value.

b = 8/2 = 4

Which topic are these words associated with? Growth, Decay, Initial Value, Exponent

• Quadratic Function

• Linear Function

• Simplifying Expressions

• Systems of Equations and Inequalities

• Exponential Function

Which topic does this image belong to?

• Systems of Equations and Inequalities

• Simplifying Expresssions

• Quadratic Function

• Linear Function

• Exponential Function