Based on common logs and base 10 exponents To see exponential growth based on natural logs and the exponent "e", click here.To read about exponential decay particularly half-life, 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 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
In 2020, it had a population of 450,000. What was its population in 2018?
We first have to calculate the annual population growth rate.
We then solve the equation by taking logs of both sides which yields: (1 + population rate) = 0.0087739243223 ÷ 10 Looking up the anti-log of 0.00087739243223 we get: 1.0020223129 which is the annual growth rate. We raise this number to the 8th power and then multiply it by the 2010 population:
(1.0020223129)^8 * 441,000 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *
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.
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