Example Suppose you won a contest and had your choice of one of these two prizes: . Prize A: $50 for the first month. The amount increases by $10 each month. How do you express increasing . Prize B: $50 for the first month. The amount increases by 10% each month. by $10 per month vs. increasing by 10% per month? To choose the correct prize, it is necessary to do the math! A. Create an equation for each situation. For prize A, you start with $50, then add a fixed amount ($10) each month. This is a constant change with a fixed amount of growth. This Month Prize A Prize B situation can best be modeled with a linear model of the form y = mx+b, Money Money where m is the rate of change and b is the initial amount. 0 $50 $50 Thus, the amount paid by Prize A after x months is given by: $60 $55 31 50 + 10x 2 370 $60.5 For prize B, you start with $50, then add 10% more each month (10% growth rate). This situation can best be modeled with an exponential $80 $66.55 growth model of the form y - a(1 + r), where a is the initial amount, r is 4 $90 the growth rate, and x is the time interval. $73.21 5 $100 $80.53 Thus, the amount paid by Prize A after x months is given by: y2 - 50(1.10) 6 $110 $88.58 7 $120 $97.44 B. Use each equation to complete the table to the right. 8 $130 $107.19 9 $140 $117.90 C. If the prize only pays for 6 months, which is the better prize? 10 O Prize A $150 $129.69 O Prize B $160 $142.66 12 $170 $156.92 D. If the prize pays for 16 months, which is the better prize? O Prize A O Prize B 18 $180 $172.61 14 $190 $189.87 15 $200 $280.86 16 $210 $229.75 lifelong Algebra 1B Module 4 LAL Algebra 1B (2-YR) Sem 4 (2022)