Exponential Decay Functions Worksheet

**Page 1**

1.

State whether the given model is an exponential growth model or an exponential decay model.

$v$ = 0.12(4)^{$t$}

a. | Exponential Growth Model | ||

b. | Exponential Decay Model | ||

c. | Both | ||

d. | None of the above |

[Substitute 0 for

= 0.12 x 1 = 0.12

[4

[Substitute 1 for

= 0.12 x 4 = 0.48

[4

[Substitute 2 for

= 0.12 x 16 = 1.92

[4

[Substitute 3 for

= 0.12 x 64 = 7.68

[4

The value of

The model

Correct answer : (1)

2.

State whether the model $y$ = 2(0.12)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential Growth Model | ||

b. | Exponential Decay Model | ||

c. | Both | ||

d. | None of the above |

[Substitute 0 for

= 2 x 1 = 2

[(0.12)

[Substitute 1 for

= 2 x 0.12 = 0.24

[(0.12)

[Substitute 2 for

= 2 x 0.12 x 0.12 = 0.028

[Expand (0.12)

[Substitute 3 for

= 2 x 0.12 x 0.12 x 0.12 = 0.002

[Expand (0.12)

The value of

The model

Correct answer : (2)

3.

State whether the model $y$ = 13(0.2)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential growth model | ||

b. | Exponential decay model | ||

c. | Both |

[Substitute 0 for

= 13 × 1 = 13

[(0.2)

[Substitute 1 for

= 13 × 0.2 = 2.6

[(0.2)

[Substitute 2 for

= 13 × 0.2 × 0.2 = 0.520

[Expand (0.2)

[Substitute 3 for

= 13 × 0.2 × 0.2 × 0.2 = 0.104

[Expand (0.2)

The value of

A quantity displays exponential decay, if it decreases by the same percent

So, the model

Correct answer : (2)

4.

State whether the model $y$ = 13(2)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential Decay Model | ||

b. | Exponential Growth Model | ||

c. | Both | ||

d. | None of the above |

[Substitute 0 for

= 13 x 1 = 13

[2

[Substitute 1 for

= 13 x 2 = 26

[2

[Substitute 2 for

= 13 x 4 = 52

[2

[Substitute 3 for

= 13 x 8 = 104

[2

The value of

A quantity displays exponential growth if it increases by the same percent in each unit of tme.

So, the model

Correct answer : (2)

5.

State whether the model $y$ = 8($\frac{1}{3}$)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential Growth Model | ||

b. | Exponential Decay Model | ||

c. | Both | ||

d. | None of the above |

[Substitute 0 for

= 8 x 1 = 8

[(

[Substitute 1 for

= 8 x

[Simplify the fraction.]

[Substitute 2 for

= 8 x

[Simplify the fraction.]

[Substitute 3 for

= 8 x

[Simplify the fraction.]

The value of

The model

Correct answer : (2)

6.

Victor gets a truck for $17000. The value of the truck decreases by 4% each year. Find the value of the truck after 3 years.

a. | $20,000 | ||

b. | $14960 | ||

c. | $15,738.58 | ||

d. | $18,392.52 |

The initial price of the truck, C is $17000.

The decay rate,

[Write exponential decay model.]

= 17000 x (1 - 0.04)

[Substitute 17000 for C, 0.04 for

= 17000 x (0.96)

[Subtract 0.04 from 1.]

= 17000 x 0.88

= 14960

[Simplify.]

The value of the truck after 3 years will be $14960.

Correct answer : (2)

7.

State whether the model $y$ = 3($\frac{7}{3}$)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential Growth Model | ||

b. | Exponential Decay Model | ||

c. | Both | ||

d. | None of the above |

The growth or decay factor 2.33 > 1

The model

Correct answer : (1)

8.

State whether the model $y$ = 6(0.83)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential Growth Model | ||

b. | Exponential Decay Model | ||

c. | Both | ||

d. | None of the above |

The growth or decay factor 0.83 < 1.

The model

Correct answer : (2)

9.

State whether the model $y$ = 8(4.09)^{$t$} is an exponential growth model or an exponential decay model.

a. | Exponential Growth Model | ||

b. | Exponential Decay Model | ||

c. | Both | ||

d. | None of the above |

The growth or decay factor is 4.09 >1.

The model

Correct answer : (1)

10.

What is the decay factor of the model $y$ = 6(0.7)^{$t$}?

a. | 0.9 | ||

b. | 0.6 | ||

c. | 0.8 | ||

d. | 0.7 |

The decay factor is (1 -

The decay factor of the model

[Compare the equations.]

Correct answer : (4)