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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.

 Apr 24, 2019
 #1
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+1

A = 500    given

find t

 

500 = 1562.5 * 10^(-.1t)

 

500/1562.5  = 10^(-.1t)

.32 = 10^(-.1t)                log both sides

log .32 = -.1t

log .32 / (-.1)  = t      (4.95 years)

-10 log (.32)

 Apr 24, 2019

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