8 A zookeeper models the median mass of infant monkeys born at their zoo, up to the age of 2 years, by the formula
$$y = a + b \log _ { 10 } x$$
where \(y\) is the median mass in kilograms, \(x\) is age in months and \(a\) and \(b\) are constants.
The zookeeper uses the data shown below to determine the values of \(a\) and \(b\).
| Age in months \(( x )\) | 3 | 24 |
| Median mass \(( y )\) | 6.4 | 12 |
8
- The zookeeper uses the data for monkeys aged 3 months to write the correct equation
$$6.4 = a + b \log _ { 10 } 3$$
8
- Use the data for monkeys aged 24 months to write a second equation.
8
- (ii) Show that
$$b = \frac { 5.6 } { \log _ { 10 } 8 }$$
8
- (iii) Find the value of \(a\).
Give your answer to two decimal places.
\section*{Question 8 continues on the next question}
8 - Use a suitable value for \(x\) to determine whether the model can be used to predict the median mass of monkeys less than one week old.
[0pt]
[2 marks]
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