8.7 Solving Problems with Exponential and Logarithmic Functions
Chapter
Chapter 8
Section
8.7
Solutions 17 Videos

If one earthquake has a magnitude of 5.2 on the Richter scale and a second earthquake has a magnitude of 6, compare the intensities of the two earthquakes.

1.36mins
Q1

Calculate the pH of a swimming pool with a hydrogen ion concentration of 6.21\times 10^{-8} mol/L.

0.31mins
Q2

A particular sound is 1 000 000 times more intense than a sound you ca just barely hear. What is the loudness of the sound in decibels?

0.57mins
Q3

The loudness of a heavy snore is 69 dB. How many times as loud as a normal conversation of 60 dB is a heavy snore?

1.42mins
Q4

Calculate the hydrogen ion concentration of each substance.

• baking soda, with a pH of 9
0.25mins
Q5a

Calculate the hydrogen ion concentration of each substance.

• milk, with a pH of 6.6
0.21mins
Q5b

Calculate the hydrogen ion concentration of each substance.

• an egg, with a pH of 7.8
0.23mins
Q5c

Calculate the hydrogen ion concentration of each substance.

• oven cleaner, with a pH of 13
0.21mins
Q5d

Calculate to two decimal places the pH of a solution with each concentration of H^+.

(a) concentration of H^+ = 0.000 32

(b) concentration of H^+ = 0.000 3

(c) concentration of H^+ = 0. 000 045

(d) concentration of H^+ = 0.005

0.43mins
Q6

Distilled water has an H^+ concentration of 10^{-7} mol/L. Calculate the pH of distilled water.

0.20mins
Q7a

Drinking water from a particular tap has a pH between 6.3 and 6.6. Is this tap water more or less acidic than distilled water? Explain your answer.

0.22mins
Q7b

The sound level of a moving power lawn mower is 109 dB. The noise level in front of the amplifiers at a concert is about 118 dB. How many times louder is the noise at the front of the amplifiers than the noise of a moving power lawn mower?

1.29mins
Q8

The intensity, I, of light passing through water can be modelled by the equation I= 10^{1-0.13x}, where x is the depth of the water in metres. Most aquatic plants require a light intensity of 4.2 units for strong growth. Determine the depth of water at which most aquatic plants receive the required light.

1.11mins
Q10

Dry cleaners use a cleaning fluid that is purified by evaporation and condensation after each cleaning cycle. Every time the fluid is purified, 2.1% of it is lost. The fluid has to be topped up when half of the original build remains. After how many cycles will the fluid need to be topped up?

1.51mins
Q13

How long will it take for $2500 to accumulate to$4000 if it is invested at an interest rate of 6.5%/a, compounded annually?

1.44mins
Q14

A wound, initially with an area of 80 cm^2, heals according to the formula A(t)= 80(10^{-0.023t}), where A(t) is the area of the wound in square centimetres after t days of healing. In how many days will 75% of the wound be healed?