Question

1 Let a = 5.2 and b = 4.7.

a Find the exact value of 3a + b3.
Xena estimates that the answer to part a is 140.
b Find the percentage error made by Xena in her estimation.

Answer 1

Part (a)

Replace every 'a' with 5.2 and replace every 'b' with 4.7

Then use your calculator to evaluate.

3a + b^3 = 3*5.2 + (4.7)^3 = 119.423

Answer: 119.423

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Part (b)

The true value is 119.423 which is the result of part (a)

The estimated value is 140

Subtract the two values

140-119.423 = 20.577

and divide that over the true value

20.577/140 = 0.14697857142858

Which, when rounded to 4 decimal places, we get 0.1470

Move the decimal place over to the right 2 spots to get 14.70%

Answer: 14.70% error (approximate)