MTH1010_04_01_4

Question

MTH1010_04_01_4

BlackTom AI · Accepted Answer

The problem describes a town population starting at 32,000 and decreasing by 1,000 people per year. This means the population as a function of time t (in years) should subtract 1,000t from the initial amount, not multiply or add in a way that increases it.

Option (a): P(t) = 32,000t − 1,000. This would imply the population scales with time t (multiplication by t) and subtracts a fixed 1,000, which does not align with a constant annual decrease from a fixed starting point. It incorrectly models growth with a time-dependent factor.

Option (b): P(t) = 32,000t + 1,000. Here again the presence of 32,000t suggests population grows proportionally with time, which contradicts the stated constant decrease. The +1,000 term does not reflect a steady reduction.

Option (c): P(t) = 32,000 − 1,000t. This matches the description precisely: an initial population of 32,000, with a linear decrease of 1,000 per year, so after t years the population is 32,000 minus 1,000 times t.

Option (d): P(t) = 32,000 + 1,000t. This describes a consistent increase over time, opposite of the given decrease, and thus is incorrect.

In summary, the correct formulation is the one that starts at 32,000 and subtracts 1,000 for each year, i.e., P(t) = 32,000 − 1,000t, corresponding to option (c).

MTH1010_04_01_4

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