Exp & Log Functions
Find the inverse of f(x) = 2^x
f⁻¹(x) = log₂(x)
Write the equation for 5% growth from an initial value of 100
y = 100(1.05)^t
Find the 5th term of the sequence: aₙ = 3n + 1
a₅ = 16
Convert 180° to radians
π radians
What is the amplitude of y = 3sin(x)?
3
What is the asymptote of f(x) = log(x - 3)?
x = 3
What is the initial value in y = 300(0.8)^t?
300
Recursive rule: a₁ = 2, aₙ = aₙ₋₁ + 4, find a₄
a₄ = 14
What is the reference angle for 150°?
30°
What is the period of y = sin(2x)?
π
Evaluate: log₁₀(1000)
3
Compare growth: y = 100(1.02)^t vs y = 80(1.05)^t — which grows faster?
y = 80(1.05)^t grows faster
Write explicit formula for geometric sequence: 2, 6, 18, ...
aₙ = 2(3)ⁿ⁻¹
Evaluate: sin(45°) exactly
√2 / 2
What is the midline of y = -2cos(x) + 4?
y = 4
Solve: 2^x = 16
x = 4
Use Newton’s Law: T(t) = 70 + (100 - 70)e^(-0.05t), find T(10)
≈ 88.2
Find sum: 5 + 10 + 20 + 40 (geometric)
75
What are the 6 trig functions of a 30° angle?
sin = 1/2, cos = √3/2, tan = 1/√3, csc = 2, sec = 2/√3, cot = √3
Does y = -sin(x) reflect over the x-axis or y-axis?
x-axis
Rewrite: log₅(x) = 3 in exponential form
x = 125
Use future value formula: FV = 1000(1 + 0.05/4)^(4×3)
≈ $1159.27
Convert to summation: 2 + 4 + 6 + ... + 20
∑ from n = 1 to 10 of 2n
Use the Pythagorean Identity: If sin(θ) = 3/5 and θ is in Quadrant II, find cos(θ)
cos(θ) = -4/5
Write an equation for a cosine graph with amplitude 2, period 2π, midline 1
y = 2cos(x) + 1