Question

Question

Question
Use the image to answer the question.

A decreasing curve with an arrow on the end is plotted on a coordinate plane. The curve begins at the point left parenthesis 0 comma 700 right parenthesis.

The value of a cell phone decreases exponentially at a rate of 24% each year after its release date. If the initial value of the phone is $700, the situation can be modeled by the equation  v(t)=700(0.76)t , where v is the value of the cell phone t years since its release date. Interpret the graph of the equation and identify the true statement.

(1 point)
Responses

As t increases, v decreases slowly at first and then quickly.
As t increases, v decreases slowly at first and then quickly.

As t increases, v increases slowly at first and then quickly.
As t increases, v increases slowly at first and then quickly.

As t increases, v decreases quickly at first and then slowly.
As t increases, v decreases quickly at first and then slowly.

As t increases, v increases quickly at first and then slowly.
As t increases, v increases quickly at first and then slowly.
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GPT-4o mini · Answer

The equation $ v(t) = 700(0.76)^t $ represents an exponential decay model for the value of the cell phone over time. The initial value is $700, and the value decreases at a rate of 24% each year. In an exponential decay function, as $ t $ (the time in years) increases, the value $ v(t) $ decreases. Specifically, the decrease in value is rapid initially and then slows down over time. This is due to the nature of exponential functions, where the quantity decreases by a fixed percentage rather than a fixed amount. Thus, the correct interpretation of the graph of the equation is: **As t increases, v decreases quickly at first and then slowly.**

Katy · Answer

I think it is the... NVM I don't know Sry

GPT-4o mini · Answer

No need to worry! It's completely understandable if you're feeling unsure. The key points to remember about the given equation $ v(t) = 700(0.76)^t $ are:

Exponential Decay: Since the value decreases at a fixed percentage (24%), the curve represents exponential decay.
Behavior Over Time: In exponential decay models, the value decreases rapidly at first, but as time progresses, the rate of decrease slows down. This means that while the phone starts losing its value quickly, the amount it loses over time becomes less and less.

So based on these points, the correct statement is:

As t increases, v decreases quickly at first and then slowly.

If you have any more questions or if there's anything else you're curious about, feel free to ask!

Katy · Answer

Hey was there a picture to go with the question?

GPT-4o mini · Answer

I apologize for the confusion, but as a text-based AI, I don't have the ability to see or interpret images. Your initial description of the graph as a decreasing curve starting at the point (0, 700) was helpful in understanding the context of the question.

If the graph or image provided has specific features or labels, you could describe them, and I’d be glad to help you interpret those details or answer any further questions!