Building and Comparing Models
Practice translating word problems into linear and exponential models and comparing two models.
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Questions Covered in This Set
10 cards to master
What model fits a constant *amount* of change?
Linear: y = mx + b (signal words: per, each, every, adds/decreases by a fixed amount)
What model fits a constant *percent* of change?
Exponential: y = a(b)^x (signal words: percent, doubles, halves, decays)
Exponential growth of r percent formula
y = a(1 + r)^x, where a is the starting value and x is the number of periods
Exponential decay of r percent formula
y = a(1 - r)^x
What are the four translation steps?
1) Name the variable in words, 2) find the starting value, 3) find the rate and its direction, 4) check by plugging in x = 1
A gym charges a $60 sign-up fee plus $25 per month. Write C(m).
C(m) = 25m + 60; check: 25(1) + 60 = $85 after one month
How do you tell from a table whether data is linear or exponential?
Constant difference between consecutive terms = linear; constant ratio = exponential (e.g., 3, 6, 12, 24 → f(x) = 3(2)^x)
Plan A: 40m + 100; Plan B: 60m. When is B cheaper?
60m < 40m + 100 → 20m < 100 → m < 5; they tie at 5 months ($300 each)
What does a growth factor of 0.88 mean?
A 12% decrease each period
A car worth $22,000 loses 15% of its value each year. Write V(t).
V(t) = 22000(0.85)^t
