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}