Question

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In a science experiment, Emma heats a beaker of water with an initial temperature of 72°F. Her data shows that the water temperature increases 12°F every minute. You can use a function to describe the water temperature x minutes after the experiment started.

Write an equation for the function. If it is linear, write it in the form f(x)=mx+b. If it is exponential, write it in the form f(x)=a(b)x.

Answer 1

Answer:

Step-by-step explanation: ask ai

Answer 2

Answer:

Since the water temperature increases linearly by 12°F every minute, we can express this relationship using a linear function in the form

f(x)=mx+b, where:

m is the slope, which represents the rate of change of the temperature (12°F per minute in this case).

b is the y-intercept, which represents the initial temperature (72°F in this case).

So, the equation for the linear function describing the water temperature

x minutes after the experiment started is:

f(x)=12x+72

Alternatively, if we were to express this relationship using an exponential function, it would take the form

f(x)=a(b)ˣ , where:

a is the initial value of the function (72°F in this case).

b is the base of the exponential function.

Since the temperature increases by a constant amount (12°F) every minute, we can express

b as

1 + change in temperature/initial temperature = 1 + 12/72 = 1 + 1/6 = 7/6

So, the equation for the exponential function describing the water temperature x minutes after the experiment started is:

f(x)=72(7/6)ˣ