Statistics show that the fractional part of a pair of flashlight batteries, P, that is still good after t hours of use is given by P=4−0.02t. What fractional part of the batteries is still operating after 200 hours of use? Express your answer as a fraction or as a decimal rounded to six decimal places.

Applying the formula, it is found that the fractional part of the batteries is still operating after 200 hours of use is of 0.003906.

The fractional part of batteries still working after t hours is an exponential function modeled by:

Then, after 200 hours, we have have that , and hence:

The fractional part of the batteries is still operating after 200 hours of use is of 0.003906.

A similar problem is given at link

Step-by-step explanation:

Given

Required

Determine P when t = 200

To do this, we simply substitute 200 for t in

Apply law of indices:

So:

becomes

As a decimal

(approximated)

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.