Exponential Function Lesson

Presentation

•

Mathematics

•

11th Grade

•

Medium

•

CCSS

HSF.LE.A.2, HSF-IF.C.7E, HSF.LE.B.5

Standards-aligned

Christine Richmond

Used 15+ times

FREE Resource

10 Slides • 17 Questions

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

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^xdetermine the y-intercept

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

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

Exponential Growth

by Christine Richmond

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