One of the fundamental uses of logarithms before the discovery of calculus, was to simplify calculations by changing time-consuming operation's like multiplication and division into addition and subtraction.
3 points
3
Question 1
1.
Complex and Familiar (3 - 4)
Show how that might have been done by rewriting the following problem in terms of log a, log b and log c
The magnitude M of an earthquake using
the Richter scale is modelled by the equation:
where I is the intensity ratio given by
Where Ic is the intensity of the ‘movement’ of the
Earth from the earthquake, and In is the intensity of
the ‘movement’ on a normal day-to-day basis.
1 point
1
Question 2
2.
Challenging and Familiar (5 - 6)
The San Francisco earthquake of 1906 measured a magnitude of 8.3 on the Richter scale. Shortly afterwards, an earthquake in South America had an intensity ratio four times greater than the San Francisco earthquake. Find the magnitude on the Richter scale of the earthquake in South America.
1 point
1
Question 3
3.
Challenging and Unfamiliar (7 - 8)
A recent earthquake in Afghanistan measured 7.5 on the Richter scale. Find how many times more intense the San Francisco earthquake was.
The US Food and Drug Administration uses this mathematical model for the number of bacteria B in food refrigerated at temperature T (°C):
The temperature in a particular refrigerator can be set anywhere between 2°C and 14°C.
1 point
1
Question 4
4.
Challenging and Unfamiliar (7 - 8)
Determine the temperature where the number of bacteria will be at a minimum.
The time taken by a jet to being its descent is given by the equation,
where x is the amount of time in minutes, that the flight takes to descend and H is the height in km above the ground level at which it beings it's descent.
If the jet begins its descent at 10 km above the ground, how long does it take the flight to land?
1 point
1
Question 5
5.
Challenging and Familiar (5 -6)
If the flight begins its descent at 10 km above the ground, how long does it take the flight to land?
A biotech company produces a new drug that consists of two key components, A and B. The drug is sold at two different rates based on the location of the buyer. The total price of the drug is determined by the ratio of components A and B in the formula.
Before the pandemic, the company used to charge $18 for every milligram of component A and $5 for component B, and a single standard dose costing $140.
But after the pandemic and the increase in demand, the company now charges $15 for every milligram of component A and $2 for every milligram of component B. The total price for one dose is now only $120.
1 point
1
Question 6
6.
Complex and Familiar (3 - 4)
What is the ratio of components A and B in the formula and how much of each component is in one dose of the drug?
1 point
1
Question 7
7.
Simple and Familiar (1 - 2)
What are the variables in this situation? Create equations to sai
1 point
1
Question 8
8.
Use logarithms to determine the value of k and find the brightness of the star at t = 4 hours.