Question

which of the exponential growth functions has a multiplicative rate of change of 4?

table 1:
\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -1 & \\frac{1}{2} \\\\ \\hline 0 & 1 \\\\ \\hline 1 & 2 \\\\ \\hline 2 & 4 \\\\ \\hline \\end{array}$$

table 2:
\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -1 & \\frac{1}{8} \\\\ \\hline 0 & 1 \\\\ \\hline 1 & 8 \\\\ \\hline 2 & 64 \\\\ \\hline \\end{array}$$

table 3:
\

$$\begin{array}{|c|c|} \\hline x & f(x) \\\\ \\hline -1 & \\frac{1}{4} \\\\ \\hline 0 & 1 \\\\ \\hline 1 & 4 \\\\ \\hline 2 & 16 \\\\ \\hline \\end{array}$$

Explanation:

Define multiplicative rate of change

$$ \text{Multiplicative rate of change } (b) = \frac{f(x+1)}{f(x)} $$

Calculate the ratio for each table

$$
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$$

Identify the correct table

$$ b = 4 \implies \text{Table 3} $$

Answer:

• (A) The first table with values \((-1, \frac{1}{2})\), \((0, 1)\), \((1, 2)\), \((2, 4)\)
• (B) The second table with values \((-1, \frac{1}{8})\), \((0, 1)\), \((1, 8)\), \((2, 64)\)
• (C) The third table with values \((-1, \frac{1}{4})\), \((0, 1)\), \((1, 4)\), \((2, 16)\) (Correct answer)