Colin buys a tv for £800. It depreciates at a rate of 1% per year. How much will it be worth in 2 years? Give your answer to the nearest penny where appropriate

708

Step-by-step explanation:

Answer

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Given:

The cost of the T.V. for Colin = £ 800.

The rate of depreciation per year = 4%

Time period = 3 years

To find:

How much will it be worth in 3 years? Give your answer to the nearest penny where appropriate.

Solution:

To solve the above-given problem, we will use the following formula:

where

A = the final value after depreciation

P = the present value

R = rate of depreciation

n = time period

Now, on substituting the given values in the formula, we get

we will round the above answer to its nearest penny where appropriate

≈ £ 708

Thus, the worth of the t.v. in 3 years will be £ 708.

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

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step-by-step explanation: