Modeling With Functions

A rubber ball dropped on a small surface takes a sequence of bounces. Each bounce is half as high as the preceding one. If the ball is dropped from a height of 64 feet, determine the exponential decay equation to model the situation.

Your dad buys a rare quitar in 2015 for $10,000. Experts estimate that its value will increase 12% per year. Use the given graph to predict approximately how many years it will take for the initial value to double.

• 4 years

• 5 years

• 6 years

• 7 years

The original value of a painting is $1400, and the value increases by 9% each year. Write an exponential growth function to model this situation.

• y=1400(1.09)^x

• y=1.09(1400)^x

• y=1400(.91)^x

• y=1.09^x

Classify the model as Exponential GROWTH or DECAY and identify the Growth or Decay factor .

• Growth of 15 %

• Decay of 15 %

• Growth of 85 %

• Decay of 85 %

Classify the model as Exponential GROWTH or DECAY and identify the time.

• Growth for 3 years

• Decay for 10 years

• Growth for 10 years

• Decay for 3 years

A new car depreciates about 15% each year. You purchase a new car for $35,000. Using the graph predict about how many years it will take for the value of the care to be $25,000.

• 7 years

• 5 years

• 2 years

• 1 year

• { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

• { 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 }

• y ≤ 10

• 0 ≤ y ≤ 10

• y ≥ 0

• { 1, 2, 3}

• {0, 1, 2, 3}

• 0 ≤ y ≤ 3

x ≥ 0

x ≤ 7

0 ≤ x ≤ 7

{ 0,1, 2, 3, 4, 5, 6, 7 }

• x ≥ 0

• x ≤ 7

• 0 ≤ x ≤ 7

• { 0,1, 2, 3, 4, 5, 6, 7 }

The admission fee at a carnival is $10. Each ride costs $1.75. Write the function rule for the cost if we go on x number of rides.

• f(x)=1.75x

• f(x)=10x 

• f(x)= 1.75x + 10

• f(x) = 10x + 1.75