Question

Which of the following situations could describe the graph?

(1 point)
Responses

Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.
Sienna buys a vintage record for $20. Its value appreciates by 20 percent each year.

There are 200 cockroaches in a building, and the population triples every day.
There are 200 cockroaches in a building, and the population triples every day.

Niall rents a bike for $20 per hour.
Niall rents a bike for $20 per hour.

Juveldy puts $20 in a high-yield savings account. His investment triples every year.
Juveldy puts $20 in a high-yield savings account. His investment triples every year.
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Answer 1

I don’t see the graph. Can you upload it or describe it? Give one or two points on the graph (the y-intercept and one other point) and say whether it’s curved or straight.

How to decide once I have that:
- If the graph is a straight line (constant slope), it matches Niall renting a bike for $20/hour (linear: cost = 20·hours).
- If the graph is curved and grows multiplicatively (exponential), it could be one of the exponential scenarios:
- If the graph starts at y = 20 (y‑intercept 20) and grows by a fixed percent each time unit, it could be Sienna’s (20 initial, 20% per year) or Juveldy’s (20 initial, triples per year). Which one depends on how steep the curve is (1.2^t vs 3^t).
- If the graph starts at y = 200 and triples each day, it matches the cockroach population (initial 200, base 3).
- Quick checks:
- If y(0) = 20, discard the cockroaches (they start at 200).
- If the y-values increase by multiplication by the same factor over equal x-steps, it’s exponential (Sienna, Juveldy, or cockroaches).
- If y increases by the same amount over equal x-steps, it’s linear (Niall).

Send the graph or its key points and I’ll pick the matching scenario(s).