Question

C. Gage bought a new car for $29,000 to use while he is away at college. The car depreciates (decreases in value) by 11% annually. If he plans to sell the car

once he graduates in four years, what will the value of the car be?

d. Ms. B and Ms. Dare writing problems for an algebra book. Ms. B started with ten problems already written and she can write six problems an hour. Ms. Dhad no

problems written, but she writes ten problems an hour. When will Ms. D have the same number of problems written as Ms. B? How many problems will they each

have written at that time?

Answer 1

a. The value of the car will be $18,195.25

b. (i) 2.5 hours

(ii) 25 problems each

Explanation:

a. To calculate the value of the car after four years, what we shall use is the exponential formula below;

F = PV( 1 - r)^t

where F is the value at year 4

PV is the present price = $29,000

r is the rate = 11% = 11/100 = 0.11

t is the time = 4 years

Substituting these values, we have;

F = 29,000(1-0.11)^4 = 29000(0.89)^4 = $18,195.25

The value of the car when he graduates will be $18,195

b. Let the number of hours it will take for both to have written the same number if problems

be x

For Ms B, the number of problems she would have written at that time will be 10 + 6(x)

For Ms D , the number of problems will be 10 * x = 10x

To get the time it will take for both to write same number of problems, we will need to equate the number of problems they would have written by hour x

Hence;

10 + 6x = 10x

10x-6x = 10

4x = 10

x = 10/4 = 2.5 hours

The number of problems would be;

For Ms B = 6(2.5) + 10 = 15 + 10 = 25

For Ms D = 10(2.5) = 25

They both would have written 25 problems at that time