Worksheet 3 graphing exponential functions answer key

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Problem 1 : 

Graph y = 3x. State the domain and range. 

Problem 2 : 

Graph the following function. State the domain and range.

y  =  2x + 1

Problem 3 : 

Graph the following function. State the domain and range.

y  =  -1/2 ⋅ 5x-2

Problem 4 : 

The first census was conducted in America in the year 1970. At that time, the population was 3, 929, 214. Since then, the population of America has grown by approximately 2.03% annually. Draw a graph showing the population growth of America since 1970.

Problem 5 : 

Graph the following function. State the domain and range. 

y  =  (1/3)x

Problem 6 : 

Graph the following function. State the domain and range.

y  =  2(1/4)x+2 - 3

Problem 7 : 

35 milligrams of caffeine is contained in a cup of green tea. Approximately 12.5% of the caffeine can be eliminated by the average teen from their per hour.   

(a) Draw a graph to represent the amount of caffeine left over after drinking a cup of green tea. 

(b) Estimate the amount of caffeine in the body of a teen ager 3 hours after drinking a cup of green tea. 

1. Solution :

y = 3x

Make a table of values. Then  plot the points and sketch the graph.  

The domain is all real numbers and the range is all positive real numbers. 

2. Solution :

y  =  2x + 1

The equation represents a translation of the graph y = 2x  one unit up. 

Make a table of values. Then  plot the points and sketch the graph.  

Domain  =  {all real numbers}

Range  =  {y | y > 1}

3. Solution :

y  =  -1/2 ⋅ 5x-2

The equation represents a translation of the graph y = 5x 

Graph y = 5x and transform the graph. 

(i)  a = -1/2; The graph is reflected in the x-axis and compressed vertically.

(ii)  h = 2; The graph is translated 2 units to the right. 

(iii)  k = 0; The graph is not translated vertically. 

Domain  =  {all real numbers}

Range  =  {y | y < 1}

4. Solution :

First, write an equation using a = 3,929,214 and r = 0.0203

y  =  3,929,214(1 + 0.0203)t

y  =  3,929,214(1.0203)t 

Now, graph the equation. 

5. Solution :

y  =  (1/3)x

Make a table of values. Then  plot the points and sketch the graph.  

The domain is all real numbers and the range is all positive real numbers. 

6. Solution :

y  =  2(1/4)x+2 - 3

The equation represents a transformation of the graph :

y  =  (1/4)x 

Examine each parameter. 

(i)  a = 2; The graph is streched vertically.

(ii)  h = -2; The graph is translated 2 units left. 

(iii)  k = -3; The graph is translated 3 units vertically. 

The domain is all real numbers and the range is all real numbers greater than -3. 

7. Solution :

Part (a) :

y  =  a( 1 - r)t

Substitute. 

y  =  35( 1 - 0.125)t

y  =  35(0.875)t

Graph the equation : 

Part (b) :

Equation from part (a) :

y  =  35(0.875)t

Substitute 3 for t. 

y  =  35(0.875)3

Use calculator. 

y  ≈  23.45

The caffeine in the body of a teenager will be about 23.45 milligrams after 3 hours.  

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