Suppose that a new employee starts working at $7.67 per hour and receives a 3% raise each year. After time t, in years, his hourly wage is given by the equation .y=$7.67(1.03)t. Find the amount of time after which he will be earning $10.00 per hour.

After what amount of time will the employee be earning $10.00 per hour?

  9 years

Step-by-step explanation:

You want to find t such that y=10.

  10 = 7.67(1.03)^t

  10/7.67 = 1.03^t . . . . . divide by 7.67

  log(10/7.67) = t·log(1.03) . . . . . . take logs

  log(10/7.67)/log(1.03) = t ≈ 8.9743 . . . . . years

After about 9 years, the employee will be earning $10 per hour.

a 4/6 = 9/12   not proportional

step-by-step explanation:

to find which are not proportional, we can use cross products

if it is true, they are proportional.   if it is not true, they are not proportional.

a 4/6 = 9/12

4* 12 = 6*9

48 = 54

not this is not proportional  

b 2/3 = 12/18  

2* 18 = 3 * 12

36 = 36

this is proportional

c 5/4 = 10/8  

5*8 = 4*10

40 = 40

this is proportional

d 7/5 = 35/25

7*25 = 5 * 35

175 = 175

is proportional

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32