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Currently, the temperature of a bowl of ramen is 57°C above room temperature. The temperature of the ramen decreases based on the function f(t) = 57(0.89)t where t represents time elapsed in minutes. Where does the graph of f(t) cross the y-axis, and what does this represent in the context of the problem?


a

f(57) = 0; the time it takes for the above-room temperature to reach 0°C


b

f(0) = 57; the time it takes for the above-room temperature to reach 0°C


c

f(57) = 0; the above-room temperature of the ramen at time t = 0


d

f(0) = 57; the above-room temperature of the ramen at time t = 0

Currently the temperature of a bowl of ramen is 57 C above room temperature The temperature of the ramen decreases based on the function f

Answer :

In the exponential function given, the answer is option d. f(0) = 57; the above-room temperature of the ramen at time t = 0

What is Exponential Function

An exponential function is a type of mathematical function that has the form f(x) = ab^x, where a and b are constants, and x is the independent variable. The variable x is usually the time, and the variable y is usually a value that changes over time.

The y-axis in the graph of f(t) represents the temperature of the ramen above room temperature. The x-axis represents the time elapsed in minutes.

The function f(t) = 57(0.89)^t represents the temperature of the ramen above room temperature as a function of time. The graph of this function will cross the y-axis at the point (0,57), which represents the temperature of the ramen at time t = 0.

Plugging t = 0 into the function f(t) = 57(0.89)^t we get f(0) = 57(0.89)^0 = 57 which represents the above-room temperature of the ramen at time t = 0.

1)

Option a f(57) = 0 is not correct because the temperature of the ramen is not zero at time t = 57, it's decreasing over time.

2)

Option b f(0) = 57 is the correct answer, it represents the above-room temperature of the ramen at time t = 0.

3)

Option c f(57) = 0 is not correct because it represents the above-room temperature of the ramen at time t = 57 which would be 0, however, it's not possible for the temperature to reach 0°C above room temperature, it will only get closer to it as time goes on.

4)

Option d f(0) = 57 is the correct answer, it represents the above-room temperature of the ramen at time t = 0.

Learn more on exponential function here;

https://brainly.com/question/2456547

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