Problem 27 of 34fun-027
The population of a town t years after 2020 is modeled by P(t)=5,000(1.2)t. According to the model, what is the population of the town in 2022?
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Solution walkthrough1:46
- In P(t)=5,000(1.2)t, 5,000 is the population in 2020 and each year multiplies it by 1.2.
- t counts years after 2020. For 2022, t=2022−2020=2, so we need P(2)=5,000(1.2)2.
- The exponent comes before the multiplication: (1.2)2=1.2×1.2=1.44.
- P(2)=5,000×1.44=7,200. Year by year: 5,000→6,000→7,200.
- Traps: 7,000 adds 1,000 twice, 12,000 multiplies by 2, and 8,640 goes on to 2023.