SOLUTION: the following problems involve arithmetic and geometric sequences. please can you help me. 1) Frank has taken a job with a starting salary of $15,000 and annual raises of 4%. wh

Question 266500: the following problems involve arithmetic and geometric sequences. please can you help me.
1) Frank has taken a job with a starting salary of $15,000 and annual raises of 4%. what will be his salary during his third year on the job?
2) A new pair of running shoes costs $70 now. assuming an annual 8% price increase, find the price 4 years from now?
3) the width of a pyramid decreases by 1.57 m for each successive 1m of height. if the width at a height of 1 m is 229.22 m, what is the width at a height of 86 m?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
problem number 1:

Frank has taken a job with a starting salary of $15,000 and annual raises of 4%. what will be his salary during his third year on the job?

during first year on the job, salary is 15,000.
during second year on the job, salary is 15,000 * 1.04 = 15,600.
during third year on the job, salary is 15,600 * 1.04 = 16,224.

that's 15,000 * 1.04^2

this assumes that the raises are given at the end of each year on the job.

if they asked what his salary was at the end of the third year, then the answer would be 15,000 * 1.04^3 = 16,872.96

since they said during, I had to assume 15,000 * 1.04^2.

problem number 2:

A new pair of running shoes costs $70 now. assuming an annual 8% price increase, find the price 4 years from now?

shoes cost 70 dollars now.
in 1 year the shoes will cost 70 * 1.08 = 75.6 dollars.
in 2 years the shoes will cost 75.6 * 1.08 = 81.648 dollars.
in 3 years the shoes will cost 88.17984 dollars.
in 4 years the shoes will cost 95.2342272 dollars.

that's 70 * 1,08^4

problem number 3:

the width of a pyramid decreases by 1.57 m for each successive 1m of height. if the width at a height of 1 m is 229.22 m, what is the width at a height of 86 m?

the change in height from 1 meter to 86 meters is 85 meters.

the width of the pyramid decreases 1.57 meters for each additional 1 meter in height.

this means the width has decreased by 85 * 1.57 meters = 133.45 meters.

229.22 meters minus 133.45 meters means that the width of the pyramid at a height of 86 meters is 95.77 meters.

to see how this works, assume the height changed from 1 meter to 3 meters.
that's a change of 2 meters.
2 * 1.57 meters = 3.14 meters.
229.22 minus 3.14 = 226.08
at 1 meters the width is 229.22 meters.
at 2 meters the width is 229.22 - 1.57 = 227.65 meters.
at 3 meters the width is 227.65 - 1.57 = 226.08 meters.

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