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A large open meadow near your city is shrinking in size because developers have started building new homes there.
The relationship between A, the area of the meadow, in hectares, and t, the elapsed time, in months, since the construction began is modeled by the following function.
A=1562.5⋅10^−0.1t
How many months of construction will there be before the area of the meadow decreases to 500 hectares?
Give an exact answer expressed as a base-10 logarithm.

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sqdancefan

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Answer:

  10·log(3.125) ≈ 4.949 months

Step-by-step explanation:

You want the value of t when A=500.

  500 = 1562.5·10^(-0.1t)

  500/1562.5 = 10^(-0.1t)

  log(0.32) = -0.1t

  t = -10·log(0.32) = 10·log(3.125)

The area will decrease to 500 hectares after 10·log(3.125) months of construction.

Answer:

^ Answer above is correct

Step-by-step explanation:

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