The question asks for the equation modeling pages p printed after t minutes, with 18/min and 6 already at t=0. The model is linear because pages add constantly at 18 per minute after the initial, emphasizing additive growth. The equation is p=18t +6, where 6 is the intercept and 18 the slope. At t=1, p=24, fitting the pattern. A common error is using exponential like $6(18)^t$, misapplying multiplicative change. In production models, use linear for constant rate additive increases from a starting point.

The question asks which equation gives the plant's height h after d days, growing at a constant rate. This is a linear model with constant additive growth of 1.5 cm per day, not exponential. Starting at 12 cm, h=12 + 1.5d fits. Build the model by adding the daily increase to the initial height. A key error is using exponential like $(1.5)^d$ for additive scenarios. Check for constant differences to confirm linear growth.

The question asks what 1.02 represents in the exponential revenue model R(d)=800(1.02)^d. The model is exponential growth because 1.02 is a constant multiplicative factor greater than 1, unlike linear's additive increases. The 1.02 means revenue multiplies by 1.02 daily, or grows 2% per day. This is calculated as growth rate = factor - 1 = 0.02. A key error is interpreting it as additive $1.02 daily. In exponential models, subtract 1 from the base to find the percentage multiplicative change.

The question asks what the 12 represents in the linear model y=1.8x +12 for earnings. The model is linear because earnings increase additively by $1.80 per hour, unlike exponential percentage growth. The 12 is the y-intercept, meaning $12 earned at 0 hours, perhaps a base pay. Substituting x=0 gives y=12 directly. A common error is thinking it's the hourly wage, which is the slope. In linear fits, interpret intercept as the additive starting value when input is zero.

The question asks for the equation best modeling points (0,100), (1,110), (2,121), (3,133.1). The model is exponential because ratios are constant at 1.1, showing multiplicative growth of 10% per unit, unlike linear constant differences. The equation $y=100(1.1)^x$ fits: at x=1, 100×1.1=110; x=2, 110×1.1=121; x=3, 121×1.1=133.1. Differences increase (10,11,12.1), confirming not linear. A key error is choosing linear like 100+10x, ignoring accelerating change. Plot or check ratios for points to identify multiplicative exponential patterns over additive linear.

The question asks for the annual percent increase in water usage from $W(t)=12000(1.03)^t$. This is exponential growth with multiplicative factor 1.03 per year. The 1.03 means 3% increase annually. Emphasize multiplicative over additive. A common error is misreading as 0.03% or adding 103%. Identify the base minus 1 for percent in exponential models.

The question asks for the predicted number of tickets sold after 6 hours using the linear model T(h) = 95h + 240. This is a linear model, characterized by constant additive increases of 95 tickets per hour, in contrast to exponential models where changes are multiplicative. Calculate by substituting h = 6: 95 × 6 = 570, plus 240 equals 810 tickets. Common errors include omitting the +240 to get 570 or adding incorrectly to reach 900 or 1110. Remember, linear growth adds a fixed amount each time, not a percentage. For test-taking, double-check substitutions in linear equations to ensure all terms are accounted for.

The question models phone battery percent B losing 12 points per hour after 100% at noon, and predicts at t=5. This is linear decay with constant subtraction of 12 per hour, emphasizing additive change over multiplicative. The equation is B=100-12t; at t=5, B=100-60=40%. Verify: at t=1, 88%; t=2, 76%, linear. Errors include exponential decay (A) or positive slope (C). Distinguish: constant differences mean linear, ratios mean exponential.

The question requires finding the exponential equation that fits a curve starting at 300 when x=0 and decaying to 75 when x=2. This is an exponential decay model, identified by constant multiplicative ratios, unlike linear models with additive differences. The general form is y = 300 × $r^x$; using x=2, 300 × $r^2$ = 75 gives $r^2$ = 0.25, so r = 0.5, yielding y = $300(0.5)^x$. A key error is confusing it with linear, like choice D, or miscalculating the base as 0.25 instead of 0.5. Another mistake might be using x/2 in the exponent, which doesn't fit the points. Emphasize checking ratios for exponential fits, and verify by plugging in given points.

The question requires interpreting the 1.15 in the exponential model C(t) = $1500(1.15)^t$ for customer growth. This is an exponential model, showing multiplicative growth by 1.15 each year, contrasting with linear additive increases. The 1.15 represents a 15% annual growth rate, as 1 + 0.15 = 1.15. Key errors include mistaking it for additive, like adding 1.15 or 15 customers yearly. Another mistake is confusing the initial value with the growth factor. When analyzing exponential models, identify the base as the multiplicative factor and convert to percentage for interpretation.