Question

teacher.
1. If the hydrogen ion concentration is a measure of the strength of an acid, how much stronger is
an acid like lemon juice with a pH of 2 than an acid like urine which has a pH of 5.5?
2. A 1998 Pontiac Grand-Am depreciates in value by 18% on average each year. If the car
originally sold for $19995 in 1998, how much would the car be worth in 2012?
3. The newest gossip spreads through Meaghann's high school like wildfire. The number of
students who have heard the news triples every two minutes, thanks mostly to texting. If the
gossip started with just one person, how long would it take before the entire school of 1200
students hears the news?

Answer 1

The three questions are illustrations of arithmetic operations and geometric progressions

(1) Acid concentration

The given parameters are:

pH of acid lemon juice = 2

pH of acid urine = 5.5

The difference between their pH is calculated as follows:

Difference = 5.5 - 2

Difference = 3.5

Multiply the difference by 10, to calculate the acidity

Acidity = 3.5 * 10

Acidity = 35

Hence, the acid like lemon juice is 35 times stronger than urine

(2) Depreciation

The depreciation is given as:

r = 18%

In 1998, the car's worth is $19995.

This is represented as:

a = 19995

2012 is 14 years from 1998.

This is represented as:

n = 14

So, the worth of the car in 2014 is calculated using:

$\mathbf{Worth =a(1 -r)^n}$

So, we have:

$\mathbf{Worth =19995 \times (1 -18\%)^{14}}$

Express percentage as decimal

$\mathbf{Worth =19995 \times (1 -0.18)^{14}}$

$\mathbf{Worth =19995 \times 0.82^{14}}$

Evaluate

$\mathbf{Worth =1243}$

Hence, the worth of the car in 2012 is $1243

(3) Spread of Gossip

The spread of the gossip is an illustration of geometric progression, where

a = 1 ---- the first term

r = 3 --- the common ratio

L =1200 --- the last term

So, we calculate the number of terms from 1 to 1200 using the following nth terms of geometric progression

$\mathbf{L = ar^{n-1}}$

This gives

$\mathbf{1200 = 1 \times3^{n-1}}$

$\mathbf{1200 = 3^{n-1}}$

Take logarithm of both sides

$\mathbf{log(1200) = log(3^{n-1})}$

Apply law of logarithm

$\mathbf{log(1200) = (n-1)log(3)}$

Divide both sides by log(3)

$\mathbf{n - 1 = log(1200) \div log(3)}$

$\mathbf{n - 1 =6.45}$

Add 1 to both sides

$\mathbf{n =7.45}$

Since the gossip spreads every two minutes.

The total time is:

$\mathbf{Total =2minutes \times 7.45}$

$\mathbf{Total =14.9\ minutes}$

Hence, it will take 14.9 minutes for the gossip to spread to 1200 students

Read more about geometric progressions at:

https://brainly.com/question/14320920