Carbon-14 is an element which loses exactly half of its mass every 5730 years. The mass of a sample of carbon-
14 can be modeled by a function, M, which depends on its age, t (in years).
We measure that the initial mass of a sample of carbon-14 is 741 grams.
Write a function that models the mass of the carbon-14 sample remaining t years since the initial
measurement.

P = 741 * 0.5 ^ (t/5730)

Step-by-step explanation:

If the Carbon-14 loses 50% of its mass for every 5730 years, we can write an exponencial equation as follows:

P = Po * (1-0.5)^t

Where t is the number of periods of 5730 years.

As we want periods of one year, we divide the time in the exponencial formula by 5730, so we have that:

P = Po * (1 - 0.5)^(t/5730)

Our inicial value is 741 grams, so that's the value of Po, so we have that:

P = 741 * 0.5 ^ (t/5730)

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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step-by-step explanation: