A dish of ice cream is left on the table in a room with a constant temperature of 70ºF. At t = 0, the temperature of the ice cream is 20ºF. Five minutes later, its temperature is 25ºF. When will it melt? (The ice cream will melt at 35ºF.)
15 minutes
16.93 minutes
11.477 minutes
47.456 minutes
There's not enough information to tell.
You have Newton's cooling formula. Plug in your data points (T(0)=20, T(5)=25) to get the constants involved. Then find when T(x) = 35.
Well, in my experience, ice cream can melt pretty quickly, especially on a warm day. So I would say it probably won't take more than 15 minutes for that delicious frozen treat to turn into a puddle. So I'll go with option A: 15 minutes. Just make sure you eat it before it's just a sad, melted mess!
To solve this problem, we can use the rate formula for temperature change:
Rate of temperature change = (Final temperature - Initial temperature) / Time
We know that the initial temperature is 20ºF, the final temperature is 35ºF, and it took 5 minutes for the temperature to increase by 5ºF.
Using the rate formula, we can calculate the rate of temperature change:
Rate of temperature change = (35ºF - 20ºF) / 5 minutes
= 15ºF / 5 minutes
= 3ºF/minute
Now, we can calculate how long it will take for the ice cream to reach 35ºF (melting point) starting from an initial temperature of 20ºF:
Time = (Final temperature - Initial temperature) / Rate of temperature change
Time = (35ºF - 20ºF) / 3ºF/minute
Time = 15ºF / 3ºF/minute
Time = 5 minutes
Therefore, it will take 5 minutes for the ice cream to melt.
The correct answer is 5 minutes.
To answer this question, we need to understand the concept of rate of temperature change and use it to find the time it takes for the ice cream to reach 35ºF (melting point). Let's break down the information provided and calculate the rate of temperature change.
1. We know that at t = 0 (initial time), the temperature of the ice cream is 20ºF.
2. Five minutes later, at t = 5 minutes, the temperature of the ice cream increases to 25ºF.
To calculate the rate of temperature change, we need to determine how much the temperature increased in a given time period. In this case, the temperature increased by 5ºF (25ºF - 20ºF) in 5 minutes.
Now let's use this rate to determine how long it will take for the ice cream to reach 35ºF (melting point).
The rate of temperature change can be calculated using the formula:
Rate of temperature change = Change in temperature / Change in time
In this case, the rate of temperature change is 5ºF / 5 minutes = 1ºF per minute.
To calculate the time it takes for the ice cream to reach 35ºF, we can use the formula:
Time = (Target temperature - Initial temperature) / Rate of temperature change
Time = (35ºF - 20ºF) / 1ºF per minute
Time = 15 minutes
Therefore, the correct answer is 15 minutes.