Algebra II: Unit 10 Review
***Suppose you deposit $1000 in an account paying 4% annual interest, compounded continuously. Use A = Pert to find the balance after 10 years.
$1491.82
At a wholesale food distribution center, the price of sugar has increased 6.3% annually since 1980. Suppose sugar cost $0.43 per pound in 1980 and this growth continues. What will a pound of sugar cost in 2017? Use y = a(1 + r)t and round to the nearest cent.
$4.12
Which statement best describes the effects on the graph of f(x) = log2 x when f(x) is replaced by1/3 f(x - 2 ) + 1?
. The graph is vertically compressed by a factor of 1/3 , horizontally translated 2 units right, and vertically translated 1 unit up.
Solve log5(4x - 1) = log5(x + 2)
1
Use log5(2)=0.4307 and log5(3)= 0.6826 to approximate the value of log5 12. Round to the nearest ten-thousandth, which is four places after the decimal point.
1.5440
Use common logarithms to approximate log9 72 to four decimal places.
1.9464
Solve ln (x + 2) = 3.
18.0855
Solve 92n = 40^4n - 7. Round to the nearest ten-thousandth, which is four places after the decimal point.
2.4922
log2 (x + 4) - log2 (x - 3) = 3
4
Which best reflects a correct conversion of an equation in exponential form to logarithmic form?
5^x = 25 and log5(25 )= x
Solve log1/8^x=-1
8
Mike and Marina were working on math homework together. They were working on solving the equation log4(x+ 4) + log4(x - 2) = 2.Mike says the solution set is {−6, 4} and Marina disagrees and says the solution set includes only the value x = 4. Which best resolves the disagreement in Mike's and Marina's answer?
Marina is correct. While -6 results from the equation solving process, you cannot use it in the equation in place of x because it would create a log of a negative number.
Which statement best describes the asymptotic behavior of the graph of the function f(x) = log x?
The graph of f(x) = log x approaches but does not cross the line x = 0.
***If the parent log function, f(x) = log2x is transformed to 1/2f (x-3), what will be the effect of the transformation on the graph of the parent function?
The graph will be vertically stretched and will shift 3 units to the right
***A particular compound decays according to the equation y = ae^-0.0736t, where t is in days. Find the half-life of this compound.
about 6.8 days
Write the equation 5^4 = 625 in logarithmic form.
log5(625)=4
Which following equation is the inverse of the function shown in the graph below?
y=3^x
Solve e^-9x <6.
{x | x -0.1991}
Solve 3^5x-1<30. Round to the nearest ten-thousandth, which is four places after the decimal point.
{x | x< 0.8192}
Solve log2 (7x - 3) log2 (x + 12).
{x>5/2}