MATH114: Quantitative Reasoning - Test 3 Formula Sheet

Growth Models

Linear Growth

New Value = Initial Value + (Growth Rate × Time)

Exponential Growth

New Value = Init × (1 + r)^t
Growth Factor (doubling): 2^(t/T_dbl)
Approx. Doubling (T_dbl): T_dbl ≈ 70 / P
Exact Doubling (T_dbl): T_dbl = log(2)/log(1+r)
Formula (doubling): New Value = Init × 2^(t/T_dbl)

Exponential Decay (Half-Life)

Decay Factor (half-life): (0.5)^(t/T_half)
Approx. Halving (T_half): T_half ≈ 70 / P
Exact Halving (T_half): T_half = log(0.5)/log(1 - r)
New Value = Init × (0.5)^(t/T_half)

Descriptive Statistics

Mean (μ or x̄)

Sum of values / Count of values

Range

Highest Value - Lowest Value

Range Rule of Thumb

Std Dev ≈ Range / 4

Normal Distribution

Standard Score (z-score)

z = (x - μ) / σ

68–95–99.7 Rule (Empirical Rule)

≈ 68% within ±1σ of mean
≈ 95% within ±2σ of mean
≈ 99.7% within ±3σ of mean

Relevant Excel Formulas

Basic Calculations

Power: =POWER(n, p) or =n^p
Log (Base 10): =LOG10(n)
Log (Natural): =LN(n)

Descriptive Statistics

Mean: =AVERAGE(range)
Median: =MEDIAN(range)
Mode (Single): =MODE.SNGL(range)
Min: =MIN(range)
Max: =MAX(range)
Range: =MAX(range)-MIN(range)
Std Dev (Sample): =STDEV.S(range)
Std Dev (Pop.): =STDEV.P(range)
Quartiles: =QUARTILE.INC(range, q)

Normal Distribution

Z-Score: =STANDARDIZE(x, μ, σ)
Area left of Z: =NORM.S.DIST(z, TRUE)
Z from Area: =NORM.S.INV(area)

Growth/Trend

Linear Forecast: =FORECAST.LINEAR(x, y's, x's)
Exponential Forecast: =GROWTH(y's, x's, new_x's)

Standard Normal (Z) Table - Percentiles

Z	Percentile	Z	Percentile	Z	Percentile	Z	Percentile
-3.0	0.13	-1.5	6.68	0	50.00	1.6	94.52
-2.9	0.19	-1.4	8.08	0.1	53.98	1.7	95.54
-2.8	0.26	-1.3	9.68	0.2	57.93	1.8	96.41
-2.7	0.35	-1.2	11.51	0.3	61.79	1.9	97.13
-2.6	0.47	-1.1	13.57	0.4	65.54	2.0	97.72
-2.5	0.62	-1.0	15.87	0.5	69.15	2.1	98.21
-2.4	0.82	-0.9	18.41	0.6	72.57	2.2	98.61
-2.3	1.07	-0.8	21.19	0.7	75.80	2.3	98.93
-2.2	1.39	-0.7	24.20	0.8	78.81	2.4	99.18
-2.1	1.79	-0.6	27.43	0.9	81.59	2.5	99.38
-2.0	2.28	-0.5	30.85	1	84.13	2.6	99.53
-1.9	2.87	-0.4	34.46	1.1	86.43	2.7	99.65
-1.8	3.59	-0.3	38.21	1.2	88.49	2.8	99.74
-1.7	4.46	-0.2	42.07	1.3	90.32	2.9	99.81
-1.6	5.48	-0.1	46.02	1.4	91.92	3.0	99.87
				1.5	93.32