Exponential & Logarithmic Models — Drills
Exponential & Logarithmic Models has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 5 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Ratio — A comparison of two quantities, like 3 cups flour to 2 cups water.
- Factor — A number that divides evenly into another.
- Growth factor — b itself. b > 1 means growth, 0 < b < 1 means decay.
- Half-life — The time for a decaying quantity to fall to half.
- Magnitude — The length of the vector, written |v|.
Factoring
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A quantity falls 9% each year. What is the decay factor?
Worked answer
0.91
1 - 0.09 = 0.91
Problem 2
A quantity grows 18% each year. What is the growth factor?
Worked answer
1.18
1 + 0.18 = 1.18
Half
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A 200 g sample has a half-life of 6 days. How many grams remain after 12 days?
Worked answer
50
12 ÷ 6 = 2 halvings
200 ÷ 22 = 50
Problem 2
A 32 g sample has a half-life of 5 days. How many grams remain after 20 days?
Worked answer
2
20 ÷ 5 = 4 halvings
32 ÷ 24 = 2
Evaluating
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
For y=200(3)t, find y when t=4.
Worked answer
16200
34=81
200 × 81 = 16200
Problem 2
For y=500(2)t, find y when t=3.
Worked answer
4000
23=8
500 × 8 = 4000
Classifying
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Is the sequence 4, 11, 18, 25 linear or exponential? Answer with one word.
Worked answer
linear
Each term adds 7
A constant difference means linear
Problem 2
Is the sequence 4, 8, 12, 16 linear or exponential? Answer with one word.
Worked answer
linear
Each term adds 4
A constant difference means linear
Working backwards
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A culture doubles every 4 hours and now has 800 cells. How many were there 12 hours ago?
Worked answer
100
12 ÷ 4 = 3 doublings
800 ÷ 8 = 100
Problem 2
A culture doubles every 3 hours and now has 1600 cells. How many were there 6 hours ago?
Worked answer
400
6 ÷ 3 = 2 doublings
1600 ÷ 4 = 400