Asymptote of the exponential decay V(t)=700(0.82)^t — laptop value approaches $0 over time

Find the horizontal asymptote for V(t)=700(0.82)^t. Explains why the laptop's value approaches $0 as t increases (exponential decay) but never actually reaches zero.

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Complete the sentences:

The equation of the function's asymptote is y = 0.

This means that over time the value of the laptop gets closer and closer to $0 but never reaches that value.

Explanation:

  1. Because 0.82 is between 0 and 1, (0.82)t approaches 0 as t increases without bound.
  2. Thus V(t) = 700(0.82)t approaches 700·0 = 0 as t → ∞.
  3. Therefore the horizontal asymptote is y = 0: the value gets arbitrarily close to $0 for large t but is never exactly $0 for any finite t.

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