Writing Exponential Equations

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

• 282 grams

• 5,366 grams

• 5 grams

• 53 grams

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.SSE.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

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

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Answer explanation

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

b = 24/12 = 2

Find a by diving 12 by b

a = 12/2 = 6

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

The cooking club has 3 original members and doubles in size each year.

Answer explanation

There are 3 original members, so a = 3.

"doubles" = x2

So, b = 2

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

CCSS.HSF.LE.B.5

Answer explanation

Find b by dividing a term by the previous term.

b = 25/100 = 0.25

Find a by dividing 100 by b

a = 100/0.25 = 400

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

Tags

CCSS.HSG.GPE.B.6

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).

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.3

CCSS.HSF.LE.B.5

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).

Tags

CCSS.HSF.LE.A.1

CCSS.HSF.LE.B.5

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

Tags

CCSS.HSF.IF.B.4

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.3