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A cake recipe says to bake the cake until the center is 180 degrees F, then let the cake cool to 100 degrees F. The table shows temperature readings for the cake.

a. Given a room temperature of 69 degrees F, what is an exponential model for this data set?

b. How long does it take the cake to cool to the desired temperature?

To create an exponential model for the data set, use the equation T(t) = a * e^(kt) + c. Find the time it takes for the cake to cool to 100°F by solving for t when T(t) = 100°F.

Explanation:

To create an exponential model for the data set, we need to find a function that represents the relationship between the temperature of the cake and time. Let's assume the temperature of the cake at time t is T(t).

Using the given information, we know that T(0) (when the cake is first taken out of the oven) is 180°F, and T(t) approaches 100°F as t increases. We can use the equation T(t) = a * e^(kt) + c, where a, k, and c are constants, to model the cooling of the cake.

Once we have the exponential model, we can determine the time it takes for the cake to cool to the desired temperature of 100°F by finding the value of t when T(t) = 100°F.

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