Theresa bought a house on 2 January 1970 for £8000 - AQA - A-Level Maths Pure - Question 8 - 2019 - Paper 2
Question 8
Theresa bought a house on 2 January 1970 for £8000.
The house was valued by a local estate agent on the same date every 10 years up to 2010.
The valuations are sho... show full transcript
Worked Solution & Example Answer:Theresa bought a house on 2 January 1970 for £8000 - AQA - A-Level Maths Pure - Question 8 - 2019 - Paper 2
Step 1
Show that $V = pq$ can be written as $\log_{10} V = \log_{10} p + \log_{10} q$
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Answer
To show that V=pq can be written as log10V=log10p+log10q, we start by taking the logarithm of both sides:
Taking logarithm on both sides: log10V=log10(pq)
Using the property of logarithms that states log10(ab)=log10a+log10b, we can rewrite the right-hand side: log10V=log10p+log10q
Thus, it is demonstrated that V=pq can be expressed as log10V=log10p+log10q.
Step 2
The values in the table of $\log_{10} V$ against $t$ have been plotted
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Answer
From the graph plotted with values of log10V against t, we observe a linear relationship between the two variables. To determine the line of best fit:
We identify two points from the given data that correspond to their respective t values and log10V values.
Calculate the gradient of the line using the formula:
slope=(x2−x1)(y2−y1), which represents the change in log10V per change in t.
Substitute the points (0, 3.90) and (30, 5.31) into this formula to find the slope:
slope=30−05.31−3.90=301.41≈0.047.
The y-intercept can be calculated by substituting one of the points into the equation of a line in the form:
y=mx+c to determine c.
