If \(\log_a(y + 2) = 1 + \log_a x\), find x in terms of y. 2. The table shows the distribution of timber production in five communities in a certain year Co...
Question 1 Report
If \(\log_a(y + 2) = 1 + \log_a x\), find x in terms of y.
2. The table shows the distribution of timber production in five communities in a certain year
| Community | Timber Production (tonnes) |
| Bibiani | 600 |
| Amenfi | 900 |
| Oda | 1800 |
| Wiawso | 1500 |
| Sankore | 2400 |
1. Draw a pie chart to represent the information.
2. What percentage of timber produced that year was from Amenfi?
3. If a tonne of timber is sold at $560.00, how much more revenue would Oda community receive than Bibiani?
Answer Details
1. Given
\[\log_a(y+2)=1+\log_a x\]
Since \(1=\log_a a\),
\[\log_a(y+2)=\log_a a+\log_a x=\log_a(ax).\]
Therefore,
\[y+2=ax\]
\[\boxed{x=\frac{y+2}{a}}\]
2(a)(i) Pie chart
Total timber production:
\[600+900+1800+1500+2400=7200\text{ tonnes}.\]
| Community | Production (tonnes) | Sector angle |
|---|---|---|
| Bibiani | 600 | \(\frac{600}{7200}\times360^\circ=30^\circ\) |
| Amenfi | 900 | \(\frac{900}{7200}\times360^\circ=45^\circ\) |
| Oda | 1800 | \(\frac{1800}{7200}\times360^\circ=90^\circ\) |
| Wiawso | 1500 | \(\frac{1500}{7200}\times360^\circ=75^\circ\) |
| Sankore | 2400 | \(\frac{2400}{7200}\times360^\circ=120^\circ\) |
2(a)(ii)
\[\frac{900}{7200}\times100\%=\boxed{12.5\%}.\]
2(a)(iii)
Difference in production:
\[1800-600=1200\text{ tonnes}.\]
Hence, the extra revenue received by Oda is
\[1200\times\$560.00=\boxed{\$672,000.00}.\]
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