MCT4C Exponential Functions

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AMDEC Mathematics Department MCT 4C - Student Goal Tracking Sheet

Name: ___________________ Unit name: Exponential Functions Goals for this unit:

1) I can apply the concepts and rules for exponents to solve exponential equations including problems from real – world situations.

2) I can use technology, when appropriate to solve questions that involve exponential functions and equations.

3) I can describe/explain the properties of exponential functions

Today’s Topic Today’s Goal

Self-Assessment Self-Reflection

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Review of necessary skills

I am able to differentiate between functions and relations, use function notation and state domain and range for a given graph.

Exponent Laws and Rational Exponents

I am able to apply the basic exponent rules to questions that contain both integer and rational exponents and rewrite exponential expressions in radical form.

Properties of Exponential Functions

I am able to identify the properties of an exponential function and explain/prove why some properties exist.

MCT4C Exponential Functions

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Solve Exponential Equations Using Common Base

I am able to identify equations that use the concept of exponents and using common base, solve each equation appropriately.

Today’s Topic Today’s Goal

Self-Assessment Self-Reflection

Did

I w

atc

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he a

ssig

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vid

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this

topic

?

Did

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Did

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Solve Exponential Equations using Technology

I am able to identify when common base cannot be used to solve and exponential equation and use the appropriate technology to solve the equation.

Applications for Exponential Functions

I can extend my knowledge of solving exponential equations to real-world situations and reflect on the reasonableness of my answer.

Pre-test reflection (How am I going to do? What am I good at? What do I need to study or improve?)

Post-test reflection (How did I do? What was I good at? What do I need to study or improve on for the exam? How am I going to do this?)

K A C T

MCT4C Exponential Functions

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U1J1 - Review of necessary skills

1) Explain the difference between a function and a relation.

MCT4C

Exponential Functions

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U1J2 - Exponent Laws and Rational Exponents

1) Simplify the following.

A) (𝑎−2𝑏3)−5 B) (𝑎2𝑏−5𝑐8)−2(𝑎4𝑏𝑐−1)3

C) (−2𝑎2)

−2

3𝑦3 D)

2

(√5𝑎2)3

2. Use 823⁄ as an example to answer the following:

A) Explain the relationship between exponential and radical notation.

B) Evaluate 823⁄ . Which format do you prefer. Explain.

MCT4C

Exponential Functions

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U1J3 - Properties of Exponential Functions

1. For the function 𝑦 = 𝑏𝑥.

A) Sketch a graph for when b>0 and when 0<b<1.

B) List properties that are similar for both graphs.

C) List properties that are different for both graphs.

2. For the function 𝑦 = 𝑏𝑥 :

A) Explain what happens to the graph when you change the base (b=2 versus b=5)

B) Explain what happens to the graph when you change the sign on the exponent.

C) Explain why you never have a y-value of 0.

MCT4C

Exponential Functions

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U1J4 - Solve Exponential Equations Using Common Base

1. Solve the equation 13(8𝑥+2) = 52 using common bases. Briefly explain each step

in your process.

2. Solve the equation (1

9)2𝑥

×1

27= 9−𝑥 using common bases. Briefly explain each

step in your process for future reference.

MCT4C

Exponential Functions

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U1J5 - Solve Exponential Equations using Technology (Desmos.com)

1. Solve the following using Desmos.com

A) 7𝑥 = 12 B) 52𝑥−1 = 45

2. Solve the following using Desmos.com. Explain your steps.

6𝑥 − 5 = 2𝑥 + 3

MCT4C

Exponential Functions

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U1J6 - Applications for Exponential Functions

1. CIBC offers an investment that pays 5% interest compounded monthly. You invested $1500 when you were younger and now it is worth $2800. Determine how many years it was invested. 2. Mitchell has a current population of 5600 people. The Town anticipates a growth rate of 5%. Determine how many years it will take for Mitchell to reach a population of 9000, assuming the rate of growth continues.