Math 1 · Unit 7 · Lesson 6 · part 2 of 5
Building the model: three ways in
A model is an equation that stands in for a real situation.
Building the model: three ways in
A model is an equation that stands in for a real situation. Building an exponential model means finding a and b from whatever the story gives you. Three ways in.
From a story
A phone costs $800 and loses 20% of its value each year. a = 800, the starting value. Losing 20% keeps 80%: b = 0.80. The model is y = 800 · 0.80x, with x in years and y in dollars.
From a table
x: 0, 1, 2, 3 and y: 50, 150, 450, 1350. a is the output at x = 0: 50. b is the ratio: 150 ÷ 50 = 3. Model: y = 50 · 3x. (Check the other ratios: 450 ÷ 150 = 3. Good.)
From two points, one at x = 0
The curve passes through (0, 12) and (1, 18). a = 12 straight from the first point. From x = 0 to x = 1 the output is multiplied once by b, so b = 18 ÷ 12 = 1.5. Model: y = 12 · 1.5x.
If the given points are not one step apart, or neither is at x = 0, the algebra waits for Unit 13. Here, one point is always at x = 0 and the other is one step over.