Write an exponential equation to represent the situation and answer the question.
a. If the cost of a loaf of bread is now $2.75 and is increasing at 5% per year, what will it cost 10 years from now?
b. The population of Flood River City is now 42,000. Experts predict the population will decrease 25% each year for the next five years. What will be the population in five years?
c. A share of Orange stock that was worth $25 in 2000 was worth $60 in 2010. What is the multiplier and percent increase?

a. $4.48¢

b. 9,967 people

ci. Multiplier: F = 25 × (1.09)^t

cii. Percent increase = 9.15%

Step-by-step explanation:

a. The equation we are going to use to calculate the future cost of bread in 5 years:

P = F/(1+r)^t

Where P is current cost, F = future cost(what we are required to calculate), r = percentage increase per year, t = time (years).

Where P = 2.75

r = 5/100 or 0.05

t = 10

F = ?

Substituting appropriately, we have:

2.75/1 = F/(1+0.05)^10

We then cross multiply

F = 2.75 × (1+0.05)^10

F = 2.75 × (1.05)^10

F = 2.75 × 1.62889

F = $4.48¢

Therefore, the bread will cost $4.48 in 10 years.

b. Here population is 42,000 people now. There's predicted 25% decrease in population every year for the next 5years. We are to calculate the expected population in 5 years. The equation that can be used to calculate the expected population:

P = F/(1 - r)^t

F = future population

P = present population

r = percentage of decrement

t = period.

Here P = 42,000

r = 25/100 = 0.25

t = 5

F = ?

Substituting accordingly:

42000 = F/(1 - 0.25)^5

Cross multiply

F = 42000 × [(1 - 0.25)^5]

F = 42000 × 0.2373

F = 9,967

The population in the next 5 years will decrease to 9,967 people.

c. Share of orange stock = $25 in the year 2000

The same share = $60 in 2010, we are required to determine the multiplier and percent increase.

Since the future value = $60, the present value = $25, the time = 2010 - 2000 = 10 years. Then we can use the formula:-

F = P × (1 + r)^t

60 = 25 × (1 + r)^10

(1 + r)^10 = 60/25

(1 + r)^10 = 2.4

1 + r = 10√2.4

1 + r = 1.0915

r = 1.0915 - 1

r = 0.0915

r = 9.15%

Therefore the multiplier is:

F = 25 × (1.09)^t

The percent increase = 9.15%

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)