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Natural Logs
Asymptote(s)
Variation
Simplify
Solve
100
Solve. Round to the nearest hundredth. ln(x) + ln(2) = 5
x=74.21
100
Find the Horizontal Asymptote(s) for the following equation y = (1/(x + 2)) - 3
y = -3
100
In _____________ variation x values increase as y values increase at a constant rate.
direct
100
This is the common denominator for the following equation 3 = (1/x) + (6/(5x)) +1
5x
100
Solve. 1/x = 5/(x - 4)
x=-1
200
Solve. Round to the nearest hundredth. e^(x-2) = 7
x = 3.95
200
This is the Horizontal Asymptote(s) for the following equation f(x) = (x-2)/(x-4)
y = 1
200
Direct variation: Find k when x = 30 and y = 2.
1/15
200
Find the common denominator for the following equation [1/(x-2)] + [1/(x^2-7x+10)] = 6/(x-2)
(x-2)(x-5)
200
Solve. 1/6x^2 + 1/6x = 1/x^2
x = 5
300
Find the inverse of f(x). f(x) = ln(x-5) + 4
f^-1(x) = e^(x-4) + 5
300
This is the Vertical Asymptote(s) for the following equation f(x) = (x^3 - x^2 - 6x)/(-3x^2 - 3x + 18)
x = -3,2
300
Inverse variation: Find k when x = 10 and y = 7.
70
300
Simplify. Identify any undefined x-values. Leave answer factored. [(4x^2-2x)/(x^2+5x+4))]/[2x/(x^2+2x +1)]
(2(x-2)(x+1))/(2(x+4)); x doesn't equal -1
300
Solve. [2/(n + 3)] - [1/n] = -6/(n^2 + 3n)
No solution. -3 is extraneous.
400
How long would it take $10 to double in value if compounded continuously at 5% interest. Round to the nearest hundredth of a year.
13.86 years
400
What is the Horizontal Asymptote(s) for the following equation f(x) = (x+4)/(-2x-6)
y = -1/2
400
Direct variation: Find y when x = 20 if x = 8 when y = 12.
30
400
Simplify. Leave answer factored. [(n-3)/(n+5)] - [(n+4)/(n-2)]
[-14(n+1)]/[(n+5)(n-2)]
400
Ed drives to school at 20 mph and drives home at 30 mph. What is his average speed for the whole trip? Round to the nearest hundredth.
24 mph
500
Lubbonium-62 has a half-life of 23 years. How much of a 473 g sample would remain after 8 years? Round to the nearest hundredth of a year.
371.67 g
500
This is the slant asymptote for the following equation f(x) = (x - 4)/(3x^2 - 5x - 9)
y = 3x + 7
500
Inverse variation: Find x when y = -4 if x = -18 when y = -5.
y = -45/2 = -22.5
500
Simplify. Identify any undefined x-values. [x/((x^2) - 1))] - [(2x-1)/(x+1)] + [3/(x+2)]
-2x^3 + 4x^2 + 7x - 5; x doesn't equal 1,-1,-2
500
Ed can paint a fence in 3 hours. Gina can paint a fence in 2 hours. How long will it take them to paint a fence if they work together? Round to the nearest hundredth of an hour.
1.2 hours