Question

The value of a newly purchased computer will decrease over time. The value of the computer can be modeled by the following function:

f(t)=200+1,200(0.73)2t,

where t is measured in years since the computer was purchased.

Use the drop-down menus to complete the explanation of how the function models the computer's value over time.

Answer 1

1) 1,400

2) 0

3) 200

Answer 2

• $1400
• 0
• 200

Explanation:

a)

Substitute 0 for t and evaluate the expression. Recognize that any value to the zero power is 1.

f(0) = 200 +1200(0.73^(2·0)) = 200 +1200·1

f(0) = 1400

When t=0, the value of the computer is 1400 dollars.

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b)

The exponential expression 1200(0.73^(2t)) has a horizontal asymptote of 0. It gets closer and closer to 0.

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c)

The exponential term gets closer to 0, so the function value gets closer to ...

f(∞) ≈ 200 +0 ≈ 200

f(t) gets closer and closer to 200.