Logarithmic scales squeeze huge ranges into small numbers: one step on the Richter scale is ten times the amplitude, and 10 decibels is ten times the intensity. Exponential models run the other way, from a rate to a value.
log 3.2 is about 0.505, so the log is about -4.495.
Change the sign.
The answer is 4.49.
Where students go wrong
Reading a difference on a log scale as a difference in size. A magnitude 7 earthquake is not a little bigger than a 6: its amplitude is ten times as large.
Also called logarithmic scales, exponential models or log models.
What you can put on this worksheet
pH
pH=−log[H+]. Find the pH when [H+]=5.8×10−8, to the nearest hundredth.→ 7.24
Decibels
L=10logI0I. A sound is 107 times as intense as I0. Find its level in decibels.→ 70 dB
The Richter scale
On the Richter scale M=logA0A. How many times as large is the amplitude of a magnitude 7.5 earthquake as one of magnitude 5.5?→ 100
Newton's law of cooling
An 88∘C cup cools in a 20∘C room. After 13 minutes it is 43∘C. When is it 31∘C, to the nearest tenth of a minute?→ 21.8 minutes
Evaluate the solution
P(t)=1+21e−0.3t550. Find P(15), to the nearest tenth.→ 446.0
The same growth per month or quarter
f(t)=2800(1.09)t, with t in years. Rewrite it with a weekly factor, to five decimal places.→ f(t)≈2800(1.00166)52t
Questions about these worksheets
Yes. Every exponential and logarithmic models sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the exponential and logarithmic models questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 6: ph, decibels, the richter scale, newton's law of cooling, evaluate the solution and the same growth per month or quarter. Tick as many as you want and set how many of each, or let it spread them evenly.
Reading a difference on a log scale as a difference in size. A magnitude 7 earthquake is not a little bigger than a 6: its amplitude is ten times as large.