Mathematics, 26.07.2019 18:00 phillipmccormick

Aworker was paid a salary of $10,500 in 1985. each year, a salary increase of 6% of the previous year's salary was awarded. how much did the worker earn from the beginning of 1985 through the end of 2010? a $45,064.64 b $256,527.63 c $576,077.38 d $621,142.02

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Note that 6% converted to a decimal number is 6/100=0.06. Also note that 6% of a certain quantity x is 0.06x.

Here is how much the worker earned each year:

In the year 1985 the worker earned $10,500.

In the year 1986 the worker earned $10,500 + 0.06($10,500). Factorizing $10,500, we can write this sum as:

$10,500(1+0.06).

In the year 1987 the worker earned

$10,500(1+0.06) + 0.06[$10,500(1+0.06)].

Now we can factorize $10,500(1+0.06) and write the earnings as:

$10,500(1+0.06) [1+0.06]= $10,500(1.06)^2

.

Similarly we can check that in the year 1987 the worker earned $10,500(1.06)^3

, which makes the pattern clear.

We can count that from the year 1985 to 1987 we had 2+1 salaries, so from 1985 to 2010 there are 2010-1985+1=26 salaries. This means that the total paid salaries are:

$10,500+10,500(1.06)^1+10,500(1.06)^2+10,500(1.06)^3...10,500(1.06)^{26}$ .

Factorizing, we have

$=10,500[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]=10,500\cdot[1+1.06+(1.06)^2+(1.06)^3+...+(1.06)^{26}]$

We recognize the sum as the geometric sum with first term 1 and common ratio 1.06, applying the formula

$\sum_{i=1}^{n} a_i= a(\frac{1-r^n}{1-r})$ (where a is the first term and r is the common ratio) we have:

$\sum_{i=1}^{26} a_i= 1(\frac{1-(1.06)^{26}}{1-1.06})= \frac{1-4.55}{-0.06}= 59.17$ .

Finally, multiplying 10,500 by 59.17 we have 621.285 ($).

The answer we found is very close to D. The difference can be explained by the accuracy of the values used in calculation, most important, in calculating $(1.06)^{26}$ .

D

Answer from: Quest

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book= $x+184$

hence, there are x+184 pages in olivia's book.

Answer from: Quest

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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Aworker was paid a salary of $10,500 in 1985. each year, a salary increase of 6% of the previous yea...