A quantity with an initial value of 9800 decays exponentially at a rate such that the quantity cuts in half every 6 days. What is the value of the quantity after 138 hours, to the nearest hundredth?

About 5043.58

Step-by-step explanation:

The standard form for an exponential decay after t time is:

Where a is the initial value, r is the rate decay, t is the time that has passed, and d is the amount of time it takes for 1 cycle.

The initial value is 9800. So a = 9800.

The quantity cuts in half. So, r = 1/2.

And it cuts in half every 6 days. For this question, we will convert this to hours. 6 days = 144 hours. So, we can let d = 144, where t will be in hours.

Therefore, our function is:

Where t is the amount of time that has passed, in hours.

Then the quantity left after 138 hours will be:

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