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A mobile phone company records their annual sales on 31 December every year. Paul thinks that the annual sales, S million, can be modelled by the equation S= ab', where a ar b are both positive constants and t is the number of years since 31st December 2015. Paul tests his theory by using the annual sales figures from 31t December 2015 to 31st Decemb 2019. He plots these results on a graph, with t on the horizontal axis and log,,S on the vertic axis. (a) Explain why, if Paul's model is correct, the results should lie on a straight line of best fit on h graph. The results lie on a straight line of best fit which has a gradient of 0.146 and an intercept on vertical axis of 0.583. (b) Use these values to obtain estimates for a and b, correct to 2 significant figures. (c) Use this model to predict the year in which, on the 31st December, the annual sales wvould fi be recorded as greater than 200 million. (d) Give a reason why this prediction may not be reliable.

A mobile phone company records their annual sales on 31 December every year. Paul thinks that the annual sales, S million, can be modelled by the equation S= ab', where a ar b are both positive constants and t is the number of years since 31st December 2015. Paul tests his theory by using the annual sales figures from 31t December 2015 to 31st Decemb 2019. He plots these results on a graph, with t on the horizontal axis and log,,S on the vertic axis. (a) Explain why, if Paul's model is correct, the results should lie on a straight line of best fit on h graph. The results lie on a straight line of best fit which has a gradient of 0.146 and an intercept on vertical axis of 0.583. (b) Use these values to obtain estimates for a and b, correct to 2 significant figures. (c) Use this model to predict the year in which, on the 31st December, the annual sales wvould fi be recorded as greater than 200 million. (d) Give a reason why this prediction may not be reliable.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A mobile phone company records their annual sales on 31 December every year. Paul thinks that the annual sales, S million, can be modelled by the equation S= ab', where a ar b are both positive constants and t is the number of years since 31st December 2015. Paul tests his theory by using the annual sales figures from 31t December 2015 to 31st Decemb 2019. He plots these results on a graph, with t on the horizontal axis and log,,S on the vertic axis. (a) Explain why, if Paul's model is correct, the results should lie on a straight line of best fit on h graph. The results lie on a straight line of best fit which has a gradient of 0.146 and an intercept on vertical axis of 0.583. (b) Use these values to obtain estimates for a and b, correct to 2 significant figures. (c) Use this model to predict the year in which, on the 31st December, the annual sales wvould fi be recorded as greater than 200 million. (d) Give a reason why this prediction may not be reliable.
Transcribed Image Text:A mobile phone company records their annual sales on 31 December every year. Paul thinks that the annual sales, S million, can be modelled by the equation S= ab', where a ar b are both positive constants and t is the number of years since 31st December 2015. Paul tests his theory by using the annual sales figures from 31t December 2015 to 31st Decemb 2019. He plots these results on a graph, with t on the horizontal axis and log,,S on the vertic axis. (a) Explain why, if Paul's model is correct, the results should lie on a straight line of best fit on h graph. The results lie on a straight line of best fit which has a gradient of 0.146 and an intercept on vertical axis of 0.583. (b) Use these values to obtain estimates for a and b, correct to 2 significant figures. (c) Use this model to predict the year in which, on the 31st December, the annual sales wvould fi be recorded as greater than 200 million. (d) Give a reason why this prediction may not be reliable.
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