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Exponential functions and graphs
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Exponential functions and graphs
Constant multiplicative change versus linear change; Non-integer powers; Context, table, graph and formula; Growth/decay factor and percentage rate; Compound interest, population, inflation, depreciation and cooling contexts
Example 1
A value starts at 2000 and grows by 5% per period for 5 periods. Find its new value. Round to 2 decimal places.
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Answer: 2552.56
- Exponential growth multiplies by 1+r each period.
- Rounded result: 2552.56.
Example 2
A machine worth $6000 depreciates by 20% each year. Find its value after 4 years. Round to 2 decimal places.
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Answer: 2457.60
- Multiply by the retention factor each year; do not repeatedly subtract the original annual amount.
- Rounded result: 2457.60.
Example 3
A population doubles every three years. After how many years is it eight times its initial size?
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Answer: 9
- Eight =23, so three doubling periods take 9 years.
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