NapkinCalc

Algebra 2

Exponentials & logarithms

continues from lesson 1 — values defined earlier in the course stay live here

Exponential growth multiplies by the same factor every period — and the logarithm asks the reverse question: how many periods to reach a target? They are the same relationship read in opposite directions.

P0=1000P_{0} = 1000 starting amount
r=0.07r = 0.07 growth rate per period — 7%
tdouble=log(2)log(1+r)t_{double} = \frac{\mathrm{log}\left(2\right)}{\mathrm{log}\left(1 + r\right)} = 10.244810.2448 periods to double (the honest version of the "rule of 72")
✓ pass abs(P0⋅(1+r)tdouble−2⋅P0)<0.000001\mathrm{abs}\left(P_{0} \cdot \left(1 + r\right)^{t_{double}} - 2 \cdot P_{0}\right) < 0.000001 after t_double periods it really has doubled
P_0 * (1 + r)^x
200040006000051015202530

growth curve — every doubling takes the SAME number of periods