Rational Exponents and Radical Signs
Evaluate without a calculator:
64^(1/2)
8
Rewrite using a single logarithm: ln a + Ln b
ln (ab)
Rewrite in logarithmic form: 7^6 = 117,649
log_7 117,649 = 6
What is the formula for the continuous change model?
A = Pe^(rt)
ln e
1
Evaluate without a calculator: (-64)^(1/3)
-4
log (a/b) - 2log a
log (1/(ab))
Rewrite in exponential form:
ln 5 ~~1.609
e^1.609 ~~5
A family has saved $22,000 to purchase a new car in five years. They expect the car to cost $24,750 at that time. The savings will be compounded continuously. What interest rate must they get for their savings to reach the amount they need?
2.36%
10^x = 155
about 2.19
Rewrite using a radical sign: v^(7/5)
root(5)(x^7)
Use the fact that log_4 6~~1.292 , evaluate log_4 216
3.876
Evaluate without using a calculator:
log 0.001
-3
What is the annual yield of a savings account with an interest rate of 5.25% compounded continuously?
e^0.0525 = 1.0539
5.39%
Find the inverse of
y = 4lnx
y = e^(x/4)
Evaluate (\frac{64}{125})^(1/3) without using a calculator
4/5
Rewrite as a single logarithm: log_b \frac{b^2}{5} + log_b 5b
log_b b^3 = 3
A radioactive substance has a half-life of 10 years. If a sample starts with 80 grams, how many years will it take for the sample to be at 10 grams?
10 = 80(1/2)^(t/10) 30 years
What is the annual yield of an account with an interest rate of 3%? Round to the nearest hundredth percent.
3.04%
Round to the nearest thousandth: log_x 6 ~~25
1.074
Rewrite using a radical sign and no negative exponents: (xy^(-4/3))^(5/7)
root(7)(x^5) / root(21)(y^20
If log a = log (c +5) -2logb , find an expression for a that does not involve logarithms.
a = (c+5)/b^2
Write an equation that can be used to solve half-life problems and state what each variable represents.
y: amount of substance left after time t
a: original amount of substance
t: years
t(half): half-life of substance
y = a(1/2)^(t/t_(half)
A high school student deposits $2,000 into a savings account with an interest rate of 8.25%, how long will it take for the account to reach $2,800?
about 4 years
20(5)^x=15