To find the percentage increase or decrease, we use the formula:
[tex]\[
\text{Percentage Change} = \left( \frac{\text{New Amount} - \text{Original Amount}}{\text{Original Amount}} \right) \times 100
\][/tex]
Let's calculate the percentage change for each case step-by-step and round the answers to one decimal place.
### Case (a)
- Original amount: 40
- New amount: 48
[tex]\[
\text{Percentage Change} = \left( \frac{48 - 40}{40} \right) \times 100 = \left( \frac{8}{40} \right) \times 100 = 20.0\%
\][/tex]
### Case (b)
- Original amount: 4000
- New amount: 3600
[tex]\[
\text{Percentage Change} = \left( \frac{3600 - 4000}{4000} \right) \times 100 = \left( \frac{-400}{4000} \right) \times 100 = -10.0\%
\][/tex]
### Case (c)
- Original amount: 1.5
- New amount: 2.3
[tex]\[
\text{Percentage Change} = \left( \frac{2.3 - 1.5}{1.5} \right) \times 100 = \left( \frac{0.8}{1.5} \right) \times 100 \approx 53.3\%
\][/tex]
### Case (d)
- Original amount: 12000
- New amount: 12400
[tex]\[
\text{Percentage Change} = \left( \frac{12400 - 12000}{12000} \right) \times 100 = \left( \frac{400}{12000} \right) \times 100 \approx 3.3\%
\][/tex]
### Case (e)
- Original amount: 12000
- New amount: 8600
[tex]\[
\text{Percentage Change} = \left( \frac{8600 - 12000}{12000} \right) \times 100 = \left( \frac{-3400}{12000} \right) \times 100 \approx -28.3\%
\][/tex]
### Case (f)
- Original amount: 9.6
- New amount: 12.8
[tex]\[
\text{Percentage Change} = \left( \frac{12.8 - 9.6}{9.6} \right) \times 100 = \left( \frac{3.2}{9.6} \right) \times 100 \approx 33.3\%
\][/tex]
### Case (g)
- Original amount: 90
- New amount: 2400
[tex]\[
\text{Percentage Change} = \left( \frac{2400 - 90}{90} \right) \times 100 = \left( \frac{2310}{90} \right) \times 100 \approx 2566.7\%
\][/tex]
Let's summarize the results in the table:
[tex]\[
\begin{tabular}{|c|c|c|c|}
\hline & \text{Original amount} & \text{New amount} & \begin{tabular}{c}
\text{Percentage increase or} \\
\text{decrease}
\end{tabular} \\
\hline a & 40 & 48 & 20.0\% \\
\hline b & 4000 & 3600 & -10.0\% \\
\hline c & 1.5 & 2.3 & 53.3\% \\
\hline d & 12000 & 12400 & 3.3\% \\
\hline e & 12000 & 8600 & -28.3\% \\
\hline f & 9.6 & 12.8 & 33.3\% \\
\hline g & 90 & 2400 & 2566.7\% \\
\hline
\end{tabular}
\][/tex]
