Question

Match each function with its corresponding logarithmic inverse function. The exponential functions are A town's population of 5,000 people increases by 2% per year, an investment of $1,200 earns 5.5% annual interest, a car brought for $20,000 loses 18% of its value each year, a radioactive sample of 50 grams decays at a rate of 10% per hour. The corresponding logarithmic inverse functions are y=1200(1.055) ^x, y=50(0.90) ^x, y=20000(0.82) ^x, y=5000(1.02) ^x.

Answer 1

Matches:

- Town population of 5,000 increasing 2% per year: y = 5000(1.02)^x
- Investment of $1,200 earning 5.5% annually: y = 1200(1.055)^x
- Car bought for $20,000 losing 18% per year: y = 20000(0.82)^x
- Radioactive sample of 50 g decaying 10% per hour: y = 50(0.90)^x

(Reason: growth uses factor 1 + r, decay uses factor 1 − r.)