Worksheet · solutions includedExponential Functions & Growth — Practice Worksheet
Try each problem first, then click Show solution. To print an answer key, open all solutions before File ▸ Print.
Section A — the questions you missed
Original — Math M1 Q14 (you answered B; correct D)
Bacteria start at 300,000 cells/mL and double every 3 hours. How many cells/mL after 15 hours?
- A.1,500,000
- B.3,000,000
- C.4,800,000
- D.9,600,000
Show solution
Number of doublings = 15 / 3 = 5.
300,000 × 25 = 300,000 × 32 = 9,600,000.
Answer: D) 9,600,000
Original — Math M1 Q19 (you answered A; correct D)
The first term of a sequence is 9. Each term after the first is 4 times the preceding term. Which equation gives the nth term w?
- A.w = 9 + 4n
- B.w = 4 · 9(n−1)
- C.w = 9 · 4n
- D.w = 9 · 4(n−1)
Show solution
Geometric: first term 9, ratio 4.
aₙ = a₁·r(n−1) = 9·4(n−1).
Check n=1: 9·40 = 9. ✓
Answer: D) w = 9 · 4(n−1)
Original — Math M2 Q10 (you answered B; correct C)
P(t) = 290·(1.0446)t models population t years after 2005. Population increases by n% every 18 months. What is n (nearest tenth)?
Show solution
18 months = 1.5 years → factor = 1.04461.5 ≈ 1.0676.
n = (1.0676 − 1)×100 ≈ 6.8.
Answer: C) 6.8
Section B — new practice (same skills)
Practice 1
A sample starts at 50 mg and triples every 4 days. Write P(t) for t in days, then find P(12).
Show solution
P(t) = 50 · 3(t/4).
P(12) = 50 · 33 = 50 × 27 = 1350 mg.
Answer: P(t)=50·3(t/4); P(12)=1350
Practice 2
The first term of a geometric sequence is 5 and each term is 2× the previous. What is the 6th term?
Show solution
a₆ = 5 · 25 = 5 × 32 = 160.
Answer: 160
Practice 3
An investment grows 3% per year. By what percent does it grow over 2 years (nearest tenth)?
Show solution
Factor = 1.032 = 1.0609.
(1.0609 − 1)×100 = 6.09 ≈ 6.1%.
Answer: ≈ 6.1%
Practice 4
A colony halves every 6 hours. What fraction of the original remains after 24 hours?
Show solution
Number of halvings = 24/6 = 4.
(½)4 = 1/16.
Answer: 1/16