Exponential Function Lesson

Exponential Growth

by Christine Richmond

​You have heard of Exponential Growth

• ​Population growth

• ​Bacteria Decay or growth

• ​Spread of Virus

• ​House Value

• ​Compound interest , making your money grow

• ​Depreciation of a car

​You will be able to...

​Explain the meaning of the coefficient, the base, and the exponent in context of real world situations

​What is exponential function used for?

​By definition it is a growth of a quantity that is not linear

Multiple Choice

Is the graph linear, exponential or neither?

• Linear
• Exponential
• Neither

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Exponential Growth
• Exponential Decay
• Linear
• None

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Growth
• Decay
• Linear
• None

Multiple Choice

As x → ∞ , f(x) →

• -4

• -3

• ∞

• -∞

​Example 1:

• ​Suppose a bucket with 100 milliliters of water in it is left out in a steady rain where it gains an extra 100 milliliters each hour. The amount of water in the bucket after t hours is modeled

Multiple Choice

What type of function is this?

• Linear

• Exponential

• Neither

• Both

​Linear

• ​Graph is a line

• ​The rate of growth of the amount of water is constant

• ​No matter how much water is in the bucket, another 100 mL gets added each hour.

• ​Linear Growth

​Example 2:

​Suppose there are 100 bacteria in the water in the bucket and in one hour the number of bacteria doubles.

​

​Why is this exponential?

​Explination

​- Function is in growth model

​-There are now twice as many bacteria in the bucket.

-During the second hour, the population doubles again.

-Now there is four times the original number.

Multiple Choice

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

Multiple Choice

Identify the initial value:

y = 6.87 (4)^x

• a = 4

• a = 6.87

• a = 3

• a = 1

Multiple Choice

Given y=3^x determine the y-intercept

• 1

• 3

• 0

• y

Multiple Choice

Which equation describes the story below?

You start with $5 and triple your money every day.

• y=5(3)^x

• y=5^x

• y=5(3x)

• y=15^x

Multiple Choice

Which of the equations below represent this table?

• y=3⋅(36)^x

• y=36⋅(3)^x

• y=3⋅(⅓)^x

• y=36⋅(⅓)^x

Multiple Choice

In an exponential function, what does the 'a' represent?

• SLOPE

• RATE OF CHANGE

• Y-INTERCEPT

• COMMON RATIO

​What if we have to deal with percent?

​What is the Initial amount (y-intercept)

​

Increase by 100%______

​

Increase by 50%​______

​

​Increase by 30% is _____

​

​Decrease by 60% is ______

​

​Decrease by 90% is ______

​

Multiple Choice

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay rate?

• ^0.08

• ^1.08

• 0.92

• 8%

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x
• y=30(5000)^x
• y=5000(1.3)^x
• y=5000x^x

Multiple Choice

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the exponential equation that models this situation?

• y = 8(15,000)^x

• y = 15,000(1.08)^x

• y = 15,000(0.92)^x

• y = 15,000(0.08)^x

Multiple Choice

Write an exponential function to model the situation. The value of a car is $18000 and is depreciating at a rate of 12% per year.

• V(t) = .88(18000)^t

• V(t) = .12(18000)^t

• V(t) = 18000(.88)^t

• V(t) = 18000(.12)^t

Multiple Choice

The equation f(x) = 300(1.06)^x is being used to calculate the amount of money in a savings account.  What does the 1.06 represent?

• 6% growth
• 6% decay
• 1.06% growth
• .06% decay

Multiple Choice

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