Exponential functions and logarithms

Presentation

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Mathematics

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University

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Practice Problem

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Medium

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CCSS

HSF.BF.B.5, HSF-IF.C.8B, HSF-IF.C.7E

Standards-aligned

Adrián Favela

Used 7+ times

FREE Resource

9 Slides • 36 Questions

Exponential functions

$f\left(x\right)=k\cdot a^x$

An exponential function

$k$ and $a$ are constant, with $k\ne0$ , $a\ne0$ , $a\ne1$

$f\left(x\right)=k\cdot a^x$

If:
$0<a<1$ , then we have exponential decay, because it's stictly decreasing

If:
$a>1$ , then we have exponential growth, because it's strictly increasing.

Multiple Choice

What type of function is y = 7(5/4)^x?

Exponential Growth

Exponential Decay

Linear

None of the above

Multiple Choice

What type of function is f(x)=2(1/7)^x ?

Exponential Growth

Linear

Exponential Decay

None of the Abovee

Multiple Choice

Is this exponential growth or decay?

Growth

Decay

Multiple Choice

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

Growth

Decay

Linear

None

Multiple Choice

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

Exponential Growth

Exponential Decay

Linear

None

Go to MathIsFun and check out the exponential function and its properties.

https://www.mathsisfun.com/sets/function-exponential.html

You can find this link in Blackboard.

Do some notes on the information on the website.

Multiple Choice

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

y=a\left(b\right)^x

SLOPE

RATE OF CHANGE

Y-INTERCEPT

COMMON RATIO

Multiple Choice

What is the growth factor of the situation represented by f(x)=10(0.3)^x?

0.3

Multiple Choice

Identify the common ratio (multiplier) of the function f(x)=2(4)^x.

(2)^x

Multiple Choice

Which of these functions represents an initial value of 20 decreasing at a rate of 30%?

$y=-30\left(20\right)^x$

$y=20\left(0.7\right)^x$

$y=20\left(0.3\right)^x$

$y=-.3x+20$

Multiple Choice

On the graph y = 2^x - 3,

what is the equation of the asymptote?

y = 0

y = 2

y = -2

y = -3

Multiple Choice

On the graph y =3^x + 4,

What is the equation of the asymptote

y = 0

y = 3

y =4

(0,3)

Multiple Choice

Identify the y-intercept (initial value) of the function f(x)=2(4)^x.

(2)^x

Multiple Choice

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

(.27)^x

.27

3.51

Application of Exponential Functions

- MathIsFun -

https://www.mathsisfun.com/algebra/exponential-growth.html

You can find this link in Blackboard.

Do some notes on the information on the website if you need to.

Multiple Choice

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

f(x)=400(1+3)^x

f(x)=400(1-0.03)^x

f(x)=400(1+0.03)^x

f(x)=400(0.03)^x

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 1.015 represent?

The number of elephants was 1,015 in 1975.

The number of elephants increases by 1.5% each year.

The number of elephants increases by 101.5% each year.

The number of elephants is multiplied by 1.015 each year.

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
What does the value 12 represent?

The predicted increase in number of elephants in the refuge each year.

The predicted decrease in number of elephants in the refuge each year.

The number of years it will take for the elephant population to stop increasing.

The initial amount of elephants in the park.

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

Increasing

Decreasing

Multiple Choice

A collectible car has been going up in price by 10% each year. If the car is already worth $29,000, how much will the car be worth in 5 years?

$0.29

$2,900,000,000

$46,704.79

$145,000

Multiple Choice

The amount of ants in a colony, f, that is decaying can be modeled by f(x) = 800(.87)^x, where x is the number of days since the decay started. By what percentage is the colony decaying?

87%

13%

800%

8.7%

Introduction to Logarithms

$y=a^x\ \leftrightarrow\ x=\log_ay$

$y=e^x\ \leftrightarrow\ x=\ln y$

A logarithm is the inverse of an exponential function. $\log_ab$

$\ln x=\log_ex$ - The Natural logarithm is represented by $\ln$ and it means a logarithm with base $e$ . Remember $e=2.71818...$

Logarithms

- MathIsFun -

https://www.mathsisfun.com/algebra/logarithms.html

https://www.mathsisfun.com/algebra/exponents-logarithms.html

You can find these links in Blackboard.

Do some notes on the information on the website if you need to.

Multiple Choice

Evaluate the following logarithm:

log₆6

Multiple Choice

Evaluate the following logarithm:

log₆36

Multiple Choice

Evaluate.
3 log₂4

Multiple Choice

Evaluate the following logarithm:

log₄16

-2

¹/₂

Multiple Choice

Evaluate the following logarithm:

log₁₆32

⁴/₃

³/₄

⁵/₄

⁴/₅

Multiple Choice

Evaluate the following logarithm:

log₁₅1

-1

¹/₂

Multiple Choice

Rewrite 3⁴ = 81 in logarithmic form.

log₃4 = 81

log₈₁3 = 4

log₃81 = 4

log₄81 = 3

Multiple Choice

Write in exponential form

log₂32 = 5

2^-5 = 32

2³² = 5

2⁵ = 32

32⁵ = 2

Multiple Choice

Write in logarithmic form

2^-4 = ¹/₁₆

log₂(¹/₁₆) = -4

log_-4(¹/₁₆) = 2

log_-4 2 = ¹/₁₆

log₂(-4) = ¹/₁₆

Multiple Choice

Rewrite log₂8 = 3 in exponential form

2⁸ = 3

2³ = 8

3² = 8

8³ = 2

Multiple Choice

Write in exponential form.
log₂(¹/₈) = -3

2^-3 = ¹/₈

2^1/8= -3

-3² = ¹/₈

-3^1/8 = 2

Multiple Choice

Write in logarithmic form.
2^-4 = ¹/₁₆

log₂(¹/₁₆) = -4

log_-4(¹/₁₆) = 2

log_-4 2 = ¹/₁₆

log₂(-4) = ¹/₁₆

Multiple Choice

Write in logarithmic form.
5² = 25

log₅2 = 25

log₂25 = 5

log₂₅5 = 2

log₅25 = 2

Multiple Choice

Write as one logarithm. Simplify, if possible.
log₃9 + log₃27

-1

Multiple Choice

Solve for x:

log₂32=3x

5/3

3/5

Multiple Choice

Solve for x.
3^x = 27

Open Ended

¿What did you learn today? - Write down your answer.

Type response here

Exponential functions

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