The current annual production of a mine is 9300 kilograms, but it is decreasing with a half-life of 6 years.

Estimate the production of the mine in 15 years using the Half-Life.

Round to the nearest WHOLE number and then enter numeric values without units and symbols.

If the answer is 1,200 kilograms, enter 1200 as your answer.

Question

The current annual production of a mine is 9300 kilograms, but it is decreasing with a half-life of 6 years.

Estimate the production of the mine in 15 years using the Half-Life.

Round to the nearest WHOLE number and then enter numeric values without units and symbols.

If the answer is 1,200 kilograms, enter 1200 as your answer.

BlackTom AI · Accepted Answer

The problem asks us to estimate future production using a half-life decay model.
First, identify the given data: current production P0 = 9300 kg, half-life T1/2 = 6 years, future time t = 15 years.
The formula for exponential decay with a half-life is P(t) = P0 * (1/2)^(t / T1/2).
Plugging in the numbers, the exponent becomes t / T1/2 = 15 / 6 = 2.5.
Thus P(15) = 9300 * (1/2)^(2.5).
Compute (1/2)^(2.5) as 1 / (2^2.5). Now 2^2.5 = 2^2 * 2^0.5 = 4 * sqrt(2) ≈ 4 * 1.41421356 ≈ 5.65685425.
Therefore P(15) ≈ 9300 / 5.65685425 ≈ 1643.6.
Rounding to the nearest whole number yields 1644.
Note on formatting: if your system requires digits only without commas, you would enter 1644; some alternatives may show 1,644 with a comma, which is the same value but the expected input here is the plain digits 1644.
To summarize the logical steps, you used the decay formula, computed the exponent as 2.5, evaluated the base power, divided by that factor, and finally rounded to the nearest integer.
Finally, be mindful of rounding at the end since intermediate decimals can influence the final whole-number entry, but here the rounding lands squarely on 1644.

ST-MATH-0824-750-49498-202503 Q3 Linear & Exp Modeling

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