Percent Change
A jacket originally costs $80. After a 25% price increase, what is the new price?
$100 = 80(1.25)
If interest is ‘compounded quarterly,’ how many times per year is it calculated and added?
4 times per year
What is the y-intercept of f(x) = 9 · (1.4)ˣ?
9 (the value when x = 0)
Does f(x) = 5 · (0.4)ˣ represent exponential growth or exponential decay?
Decay, the base 0.4 is between 0 and 1
A bakery sells 50 loaves on Day 1. Sales triple each day. How many loaves are sold on Day 3?
450 loaves (50 · 3² = 450)
A population of 400 deer grows by 8% each year. Write an expression for the population after t years.
400 · (1.08)ᵗ
$600 is invested at 5% annual interest, compounded annually. What is the balance after 1 year?
$630
An exponential graph passes through (0, 3) and (1, 15). What is the function?
f(x) = 3 · 5ˣ
A quantity DECREASES by 40% each year. What base would you use in its exponential function?
0.60 (since 1 − 0.40 = 0.60)
A phone starts at 100% battery and loses 20% of its charge each hour. What percent remains after 2 hours?
64% (100 · 0.8² = 64)
A car loses 15% of its value every year. If it is worth $30,000 today, what is next year’s value?
Multiplier: 0.85 → Next year: $25,500
Write the formula for $2,000 invested at 6% annual interest compounded semi-annually after t years.
A = 2000 · (1.03)^(2t)
f(x) = a · bˣ passes through (0, 4) and (2, 36). Find a and b.
a = 4, b = 3
For large x, which grows faster: f(x) = 1000x or g(x) = 3ˣ? Explain why.
g(x) = 3ˣ — exponential functions always eventually outgrow any polynomial
A video has 200 views and views increase by 50% every hour. Write a function V(t) for views after t hours.
V(t) = 200 · (1.5)ᵗ
f(x) = 7 · (0.62)ˣ, by what percentage does f decrease each time x increases by 1?
38% decrease per step (since 1 − 0.62 = 0.38)
$500 is invested at 12% annual interest compounded monthly. What is the growth factor for a single month?
1.01 (since 12% ÷ 12 = 1% per month)
For f(x) = 80 · (0.5)ˣ, find the value of x when f(x) = 10.
x = 3 (80 · 0.5³ = 10)
A substance loses half of its mass in 1 year. Starting with 200 g, write a function A(t) for the remaining amount.
A(t)=200 * (0.5)t
A patient takes 500 mg of medicine that decreases by 30% per hour. How much remains after 4 hours?
≈120 mg (500 · 0.7⁴ ≈ 120)
A town grew from 12,000 to 14,520 people in exactly 2 years at a constant annual rate. What is the annual growth rate percentage?
10% per year (12,000 · 1.1² = 14,520)
After 4 years, an investment of 1000 with a 5% interest rate will be worth about how much?
~$1,216
The graph of f(x) = a · bˣ passes through (1, 12) and (3, 108). Find a and b.
b = 3, a = 4 (check: 4·3=12, 4·27=108)
Option A: Save $400, add $8/year (linear). Option B: $300, grow 8%/year (exponential). After how many complete years does Option B first exceed Option A?
4 years
A scientist starts an experiment with 50 bacteria. The count triples every 4 hours. Write a function B(t) for the number of bacteria after t hours, then find how many there are after 12 hours.
B(t) = 50 · 3^(t/4); after 12 hours: 50 · 3³ = 1,350 bacteria