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A savings account starts with 1000 dollars and grows by 8 percent each year: after n years it has…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A savings account starts with 1000 dollars and grows by 8 percent each year: after years it has dollars. Draw the amount for from 0 to 30 in two panels, one with a linear scale and one with a log scale. In which year is the amount first at least double the start?
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. An array of years, the formula on the whole array, and two axes. The first year with the amount at least 2000 is found with a mask and the first place of it.
Check. , which is just below 2, and . So the amount first reaches 2000 in the year 10. The exact doubling time is years. The log panel is a straight line, because growth by the same percent each year is exponential.
Answer: in year 10, with 2158.92 dollars. The doubling time is 9.01 years.
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