The value of a car is 18,500. it loses 10.3% of its value every year. find the approximate monthly decrease in value. round your answer to the nearest tenth

$158.8

Step-by-step explanation:

There are 12 months in 1 year.

If in 1 year, it looses value of 10.3%, so in a month it will loose value of:

10.3%/12 = 0.8583% per month

So, to find the decreased value (in dollars) per month, we got to find 0.8583% of 18,500 dollars.

First, we need to convert percentage to decimal by dividing by 100. Then we multiply that to 18,500 to get our answer. So:

0.8583% = 0.8583/100 = 0.008583

Now,

0.008583 * $18,500 = $158.7855

Rounded to nearest tenth (1 decimal pae) = $158.8

step-by-step explanation:

part a. the differences are decreasing, so we know the sequence is not arithmetic. the ratios are constant (=3/4), so we know the sequence is geometric.

part b. from part a, we know the common ratio is 3/4, so each term is 3/4 of the one before. the initial term is the number of gallons at h=1.

g[h] = (3/4)·g[h-1]

g[1] = 384 . . . . initial value required for a recursive definition

part c. the general formula for a geometric sequence is

a[n] = a[1]·r^(n-1)

we have a[1] = 384, r = 3/4, and the term number given by h. the formula that follows is

g[h] = 384·(3/4)^(h-1)

part d. filling in the value and doing the arithmetic, we have

g[12] = 384·(3/4)^11 ≈ 384·0.042235136 ≈ 16.2183 . . gallons

part e. each gallon is 4 quarts, so

16.2183 gal × 4 qt/gal = 64.8732 qt