Once you decide where the maximum occurs for $x \ge 0$, plug that $x$-value into each function to find its maximum output.

Compare the maximum output you found to the numbers that appear directly in the equation (constants and coefficients). Does the maximum value show up exactly as one of these numbers, or does it only appear after simplifying?

In function I, the exponent is $(x+1)$, not just $x$. How does that extra $+1$ in the exponent affect the maximum output compared with the visible coefficient 14?

In Desmos, enter f(x)=14*7^(-(x+1)) {x>=0} and g(x)=2*7^(-x) {x>=0} so that both functions are drawn only for $x \ge 0$.

Use the trace tool or create a table for each function and look at the $y$-values near $x=0$. Note the highest $y$-value each graph attains on $x \ge 0$ and compare that value to the constants or coefficients in each equation.

Look at the coefficient and constants in each equation (14 and the exponent $(x+1)$ in the first, 2 in the second) and decide which equation has a constant or coefficient that exactly matches the maximum $y$-value you observed in Desmos.

Both functions involve the factor $7^{-x}$ (or something very close to it). Since $7>1$:

• $7^x$ increases as $x$ increases.
• Therefore $7^{-x}=\frac{1}{7^x}$ decreases as $x$ increases.

Because $x \ge 0$ and the functions are decreasing, the maximum value of each function on this domain will occur at the smallest allowed $x$, which is $x=0$.

Evaluate each function at $x=0$.

For I:

For II:

Since each function is decreasing for $x \ge 0$, these values at $x=0$ are the maximum values of $f$ and $g$ on the given domain, and both maxima are 2.

The question is not asking which function has the larger maximum. Instead, it asks:

Does the equation, as written, show the maximum value directly as one of its constants or coefficients?

So we must look at the form of each equation and see whether the number 2 (the maximum value) appears clearly as a coefficient or constant, without algebraic rewriting.

Equation I is

From Step 2, we know the maximum value of $f(x)$ is 2, but in this equation:

• The visible constant multiplier is 14.
• The exponent is $(x+1)$, which means $7^{-(x+1)}$ is always less than or equal to $7^{-1}=\frac{1}{7}$ for $x \ge 0$.

The maximum value 2 comes from both the 14 and the $7^{-(x+1)}$ together; 2 does not appear directly as a standalone constant or coefficient in this form. So equation I does not display its maximum value as a constant or coefficient.

Equation II is

From Step 2, the maximum value of $g(x)$ on $x \ge 0$ is 2, which is achieved at $x=0$ because $7^{0}=1$.

In this equation, the number 2 is a clear coefficient in front of $7^{-x}$, and this coefficient is exactly the maximum value of the function on the given domain.

• Equation I does not show the maximum value directly as a constant or coefficient.
• Equation II does show the maximum value directly as a coefficient.

Therefore, the correct answer is II only.