Step: 1

Let y be the profit made by the company after n years.

Step: 2

Profit made by the company in 1992 was $122 million.

Step: 3

The exponential growth rate, r is 0.3%.

Step: 4

[Write exponential growth model.]

Step: 5

= 122(1 + 0.003)^{n}

[Substitute C = 122, r = 0.003 and t = n .]

Step: 6

= 122(1.003)^{n}

[Simplify.]

Step: 7

So, the profit made by the company after n years will be $122(1.003)^{n} million.

Correct Answer is : 122(1.003)^{n}

Step: 1

Let y be the profit.

Step: 2

The initial profit in the business is $12143.

Step: 3

The rate of increase of profit, r is 2% or 0.02.

Step: 4

The number of years, t is 7.

Step: 5

[Write exponential growth model.]

Step: 6

[Substitute C = 12143, r = 0.02 and t = 7.]

Step: 7

[Add.]

Step: 8

So, the equation for the profit is y = 12143(1.02)^{7}.

Correct Answer is : y = 12143(1.02)^{7}

Step: 1

Let y be the value of the bike.

Step: 2

Let t be the number of years of ownership.

Step: 3

The initial value of the bike C is $4300.

Step: 4

The decay rate r is 13% or 0.13.

Step: 5

[Write exponential decay model.]

Step: 6

= 4300(1 - 0.13)^{t}

[Replace C with 4300 and r with 0.13.]

Step: 7

= 4300(0.87)^{t}

[Subtract 0.13 from 1.]

Step: 8

The exponential decay model is y = 4300(0.87)^{t}.

Correct Answer is : y = 4300(0.87)^{t}

Step: 1

The initial value of the machinery, C is $29000.

Step: 2

The decay rate, r is 3% = 0.03.

Step: 3

The exponential decay can be modeled by the equation y = C(1 - r )^{t}.

Step: 4

[Replace C with 29000, and r with 0.03.]

Step: 5

[Subtract 0.03 from 1.]

Step: 6

The exponential decay model that represents the depreciation of the machinery is y = 29000(0.97)^{t}.

Correct Answer is : y = 29000(0.97)^{t}

Step: 1

The initial value of the refrigerator C is $4000.

Step: 2

The decay rate r is 5% or 0.05.

Step: 3

The exponential decay can be modeled by the equation y = C(1 - r )^{t}.

Step: 4

[Replace C with 4000, and r with 0.05.]

Step: 5

[Subtract.]

Step: 6

The exponential decay model that represents the situation is y = 4000(0.95)^{t}.

Correct Answer is : y = 4000(0.95)^{t}

Step: 1

Let y be the length of the hair during the first six weeks and t be the number of days.

Step: 2

[Write exponential growth model.]

Step: 3

= 0.23(1 + 0.1)^{t}

[Replace C = 0.23 and r = 10% = 0.1.]

Step: 4

= 0.23(1.1)^{t}

[Add.]

Step: 5

The model for the length of the hair in first six weeks is y = 0.23(1.1)^{t}.

Correct Answer is : y = 0.23(1.1)^{t}

Step: 1

Let y be the profit.

Step: 2

The initial profit in the business, C is $13333.

Step: 3

The rate of increase of profit, r is 4% or 0.04.

Step: 4

The number of years, t is 8.

Step: 5

[Write exponential growth model.]

Step: 6

[Substitute C = 13333, r = 0.04 and t = 8.]

Step: 7

[Add.]

Step: 8

So, the exponential growth model for the profit is y = 13333(1.04)^{8}.

Correct Answer is : y = 13333(1.04)^{8}

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