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Using Logarithms in Context
1) Determine which formula to use (exponential
growth, exponential decay, compound interest, or
continuously compounded interest)
2) Set up your equation using the information in the
word problem.
3) Switch equation into logarithmic form in order to
solve for the variable in the exponent! (Use
desmos to evaluate logs!)
Examples:
1) Exponential growth:
A petri dish has 900,000 bacteria in it. Scientists know
that it grows by 12% each minute. How many minutes will
it take for the bacteria to double?
2) Exponential decay:
A lumber company has 1,200,000 trees. They plan to
harvest 7% of the trees each year. How many years will it
take to harvest half of the trees?
3) Compound interest:
Timmy wants a car that costs $14,000. He puts $9,056
into an account, which gets 5% interest compounded
quarterly. How long will it take for Timmy to have enough
money in the account to buy the car?
4) Continuously compounded interest:
An account had an initial investment of $5,000 and has
an interest rate of 9% compounded continuously. It now
has 11,525. How long has it been?
6)__________________________
Groot wants to buy baby Yoda a birthday gift that costs
$21,999. Groot puts $17,056 into an account, which gets
11% interest compounded twice a year. How long will it
take for Groot to have enough money in the account to
buy the gift???
7) _____________________________
The virus that hit exponential island has reached the
mainland. Scientists know that 12,500 people are
currently infected. Based on past data, we know that the
number of people who are infected increases by 7% each
day! How many days will it take for the number of cases
to triple?
5)____________________________
Dwight’s beet farm has 135,000 beets. He plans to
harvest 13% of the beets each year. How many years will
it take him to harvest half of his beets?
8) _________________________________
An account had an initial investment of $1 and has an
interest rate of 60% compounded continuously. It now
has $10,000! How long has it been?