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Half Life
Continuously Compounded Interest
Solving Exponential Equations
Solving Logarithmic Equations
Solving Logarithmic Equations Using Log Properties
100
The half life of sodium-22 is 2 years. How much of a 25 gram sample of sodium-22 is left after 8 years? (Round to 4 decimal places).
1.5625 grams of sodium-22 are left after 8 years
100
If you invest $100 in a bank account with 15% annual interest compounded continuously, how much will be in your account in 20 years?
About $2008.55 will be in your account in 20 years.
100
3n-2=27
n=5
100
log25n = 3/2
n=125
100
log35 + log3x = log310
x = 2
200
The half life of radioactive iodine used in medical studies is 8 hours. How much of a 100 gram radioactive iodine sample is left if it were left sitting in a lab for 2 days?
1.5625 grams of radioactive iodine are left after 2 days.
200
Supposed you decide to start a savings account with $344 left over from your last paycheck. You choose an account with 8% annual interest compounded continuously. How much money will be in your account in 15 years?
About $1142.12 will be in your account in 15 years.
200
5n-3=1/25
n=1
200
log3(4x-5) = log32x
x = 5/2
200
log724 - log7(y+5) = log78
y = -2
300
The half life of an unknown substance to be studied is 1.5 days. If a 120 gram sample was first received in New York City on Monday morning, and arrived in San Francisco for research on Saturday night, how much of the substance was left when researchers in San Francisco received it?
There was 7.5 grams of the unknown substance left when it arrived in San Francisco.
300
You win a lawsuit with McDonalds for burning yourself with hot coffee. The lawsuit awards you $1,000,000. You decide to take a fourth of that money and invest it into a retirement account with 5% annual interest compounded continuously. How much will be in the account in 25 years?
About $679,570.46 will be in the account.
300
10x-1=1002x-3
x = 5/3
300
log6(2x-3) = log6(x+2)
x = 5
300
log6(a2+2) + log62 = 2
a = 4, -4
400
A geologist examining a meteorite knows the half life of the sodium-22 inside the meteorite is 8 hours. If the meteorite hit earth at 12:30 am. on Tuesday morning, and the geologist received the meteorite, (which now contained only 10 grams of sodium-22) on Wednesday at 4:30pm., how much sodium-22 did the meteorite contain when it first hit earth?
There was originally about 113.14 grams of sodium-22 in the meteorite
400
You win the grand prize of $500,000 from a scratcher lottery ticket. Your accountant recommends that you invest 15% of the prize money into a savings account. If you take his advice and invest the money into an account with an 8% annual interest rate, compounded continuously, how many years will it take your new savings account to reach $200,000? How much money did you initially deposit?
It will take about 13 years to reach $200,000 with an initial deposit of $75000.
400
35x*811-x=9x-3
x=10
400
log7(16+2x) = log7(x2-4x)
x = 8, -2
400
log30.1 + 2log3x = log32 + log35
x = 10
500
Mercury-137 is used for kidney scans and has a half life of 3 days. The hospital orders some Mercury-137, but takes 9 days to arrive. Once it arrives, it sits in the hospital for another day, before being used on a patient. If the amount used in the patients' kidney scan was 2 grams, and 5 grams were still left over, how much Mercury-137 was originally ordered?
About 70.56 grams of Mercury-137 was originally ordered.
500
In 2015, your family of 4 competes on a TV game show and wins $200,000. The IRS takes away 25% of the total prize money in taxes. The remaining prize is split evenly between each family member. You decide to take 40% of your share and start a savings account with a 9% annual interest rate compounded continuously. How much will be in your account in 2030?
About $57861.38 will be in your account in 2030.
500
49x=7x2-6
x = -3, 5
500
log2x = log2(x2-6)
x = 3
500
Solve for n. loga4n - 2logax = logax
n = x3/4