A coffee is sitting on Mr. Frank's desk cooling. It cools according to the function T = 70(1 -0.20)^x, where x is the time in minutes and T is the temperature in
degree Celsius.
What is the initial temperature of the coffee?

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Ответ:

krystynas799

17.04.2022

Mathematics

The hourly ratio is $60 per hour, and the initial amount charged would be $30.

Step-by-step explanation:

In this problem, we just have to find the linear relation that model this situation, where the rate would be the slope, and the initial amount would be the y-axis interception. So, basically we have to find the slope-intercept form of this linear relation.

First, we finds the slope using the two given points:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{210-90}{3-1}=\frac{120}{2}=60$

Now, using one point, the slope and the point-slope form, we have:

$y-y_{1}=m(x-x_{1})\\ y-90=60(x-1)\\y=60x-60+90\\y=60x+30$

Therefore, the hourly ratio is $60 per hour, and the initial charge would be $30.

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A coffee is sitting on Mr. Frank's desk cooling. It cools according to the function T = 70(1 -0.20)^x, where x is the time in minutes and T is the temperature in degree Celsius. What is the initial temperature of the coffee?