Question

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here is taylors sketch.
what mistake, if any, did taylor make?
the horizontal asymptote should be at the line ( y = 500 ).
taylor did not make a mistake.
the ( y )-intercept should be at ( (0, 35, 500) ).
the curve should be increasing showing exponential growth

Explanation:

To determine Taylor's mistake, we analyze each option:

• The first option about \( y = 500 \) as a horizontal asymptote is incorrect without context (the graph shows \( y = 0 \) as a possible asymptote for a decay curve).
• The third option: If the context is an exponential decay (e.g., for a quantity like a radioactive substance or depreciation), the \( y \)-intercept (initial value) might be \( (0, 35500) \), but the graph's \( y \)-intercept seems too low. Wait, re - evaluating: For many exponential decay models (e.g., \( y = a(b)^x \), \( 0 < b<1 \)), the horizontal asymptote is \( y = 0 \) (correct for Taylor's graph). But if the initial value ( \( y \)-intercept) should be \( (0, 35500) \), and the graph's \( y \)-intercept is not that, then this is a mistake. The fourth option is wrong because the curve is decreasing (exponential decay), not increasing (growth). The second option is wrong. So the mistake is that the \( y \)-intercept should be at \( (0, 35500) \).

Answer:

The \( y \)-intercept should be at \( (0, 35,500) \). (The option: The \( y \)-intercept should be at \( (0, 35,500) \))