Unit 10 · Exponential Functions
Linear functions add; exponential functions multiply. Growth uses b > 1; decay uses 0 < b < 1.
Increase by 6% → multiply by 1.06. Decrease by 15% → multiply by 0.85. The general form is y = a · b^x, where a is the starting value.
A function with constant multiplicative rate of change, often y = a·b^x.
Example: A bacteria count B = 40(2)^t doubles every time period.
Try the prompt first. The steps stay folded until you ask to see them.
A subway ridership of 200,000 grows 3% per year. Write a model for year t.
Watch for
Using 0.03 as the base for 3% growth
You keep 100% and add 3%.
Fix: Growth factor = 1 + r.
Submit each answer to check it. The key is not shown until you do.
Mike uses the equation b = 1300(2.65)ˣ to determine the growth of bacteria in a laboratory setting. The exponent represents
On an island, a rare breed of rabbit doubled its population each month for two years. Which type of function best models the increase in population at the end of two years?
The third term in a sequence is 25 and the fifth term is 625. Which number could be the common ratio of the sequence?
Build two tables side by side: +5 each row vs ×2 each row.
Compare an arithmetic sequence with a geometric sequence using first differences vs. ratios.
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