Based on common logs and base 10 exponents To see exponential growth based on natural logs and the exponent "e", click here.
Using the calculator is quite simple:
What was the bacteria population at the beginning of the experiment (five hours ago.)?
^{time}
Beginning Amount = 70,000 ÷ (1.3) Beginning Amount = 70,000 ÷ 3.71293 Beginning Amount = 18,853 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
What will be its population in 2020?
^{time}
Ending Amount = 319,600 × (1.0093) Ending Amount = 319,600 × 1.0768672915 Ending Amount = 344,200 (rounded) * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
What is the annual interest rate of this account?
^{(log[Ending Amount / Beginning Amount] ÷ time)} -1We don't have actual numbers so we will substitute 1,000 for beginning amount and 2,000 for ending amount.
Rate = 10
Rate = 10
Rate = 10 Rate = 8.005973889231% * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
How long will it take the population to triple? (That is, when will the population be 21,000?)
first must solve for the rate.Rate = 10 ^{(log[Ending Amount / Beginning Amount] ÷ time)} -1For every 3 hours, we see that the population increases by a factor of 13,026 / 7,000
Rate = 10
Rate = 10
Rate = 10 Rate = 0.229997828197444
Time = log(ending amount / beginning amount) ÷ log (1 + rate) Time = log(21,000 / 7,000) ÷ log (1.229997828197444) Time = 0.477121254719662 ÷ 0.0899043446079357 Time = 5.30698774125259
rate function, enter the numbers, and then use this rate calculation after we click the time function.
Answers are displayed in scientific notation and for easier readability, numbers between .001 and 1,000 will be displayed in standard format (with the same number of significant figures.) The answers should display properly but there are a few browsers that will show no output whatsoever. If so, enter a zero
in the box above. This eliminates all formatting but it is better than seeing no
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