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Grade 11 Challenge: Modelling with Exponentials & Logs Worksheet with Answers

Grade 11 (US) · Year 12 (UK) · Class 11 (India) · Math

Unit 8: Going FurtherReal-World ChallengesChallenge

Exponentials and logs in the real world: carbon dating, earthquakes, decibels, cooling coffee and medicine doses. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Challenge: Modelling with Exponentials & Logs

Grade 11 · Math

Score___ / 12

Name

Class

Date

Learning goal: Real-World Challenges

Directions: Solve each problem. Show your work, then write your answer in the box.

Example

Cases of a new illness double every 2 days. How many days does it take to go from 1000 cases to 100000 cases? Give your answer to 1 decimal place.

Answer: 13.3

1
Cases of a new illness double every 2 days. How many days does it take to go from 100 cases to 1000 cases? Give your answer to 1 decimal place.
Show your work
Answer
2
A bone has 10% of the carbon-14 it had when the animal died. Carbon-14 has a half-life of 5730 years. How old is the bone, to the nearest 100 years?
Show your work
Answer
3
Cases of a new illness double every 4 days. How many days does it take to go from 250 cases to 250000 cases? Give your answer to 1 decimal place.
Show your work
Answer
4
One machine makes 90 dB of noise. Sound level is L = 10·log₁₀(I/I₀). How loud are 100 identical machines running together, in dB to 1 decimal place?
Show your work
Answer
5
Cases of a new illness double every 3 days. How many days does it take to go from 250 cases to 25000 cases? Give your answer to 1 decimal place.
Show your work
Answer
6
Each step of 1 on the Richter scale means the ground shakes 10 times harder and releases about 10^1.5 times more energy. How many times more energy does a magnitude 6.0 quake release than a magnitude 4.0 quake? Round to the nearest whole number.
Show your work
Answer
7
Each step of 1 on the Richter scale means the ground shakes 10 times harder and releases about 10^1.5 times more energy. How many times more energy does a magnitude 6.6 quake release than a magnitude 4.6 quake? Round to the nearest whole number.
Show your work
Answer
8
Each step of 1 on the Richter scale means the ground shakes 10 times harder and releases about 10^1.5 times more energy. How many times more energy does a magnitude 6.3 quake release than a magnitude 4.3 quake? Round to the nearest whole number.
Show your work
Answer
9
A patient takes 100 mg of a medicine every 8 hours. Its half-life in the body is 8 hours. After many doses, how many mg are in the body right after a dose? Give your answer to 1 decimal place.
Show your work
Answer
10
One machine makes 63 dB of noise. Sound level is L = 10·log₁₀(I/I₀). How loud are 2 identical machines running together, in dB to 1 decimal place?
Show your work
Answer
11
A bone has 50% of the carbon-14 it had when the animal died. Carbon-14 has a half-life of 5730 years. How old is the bone, to the nearest 100 years?
Show your work
Answer
12
Coffee at 90 °C is left in a 20 °C room. After 10 minutes it is 50 °C. Using Newton's law of cooling (the difference from room temperature shrinks by the same factor every 10 minutes), what is its temperature after 20 minutes? Give °C to 1 decimal place.
Show your work
Answer

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/11/challenge_exponential_world

Answer key (click to show)

1.6.6
2.19000
3.39.9
4.110.0
5.19.9
6.1000
7.1000
8.1000
9.200.0
10.66.0
11.5700
12.32.9

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