The function f(t) = 349.2(0.98)t models the relationship between t, the time an oven spends cooling and the temperature of the oven. For which temperature will the model most accurately predict the time spent cooling? 0 100 300 400

The function f(t) = 349.2(0.98)^t is an exponential decay function, where 349.2 represents the initial temperature of the oven in some unit (let's assume degrees Celsius for this example), and 0.98 is the base of the exponent, representing the rate at which the temperature decreases over time t.

The question asks at which temperature the model will most accurately predict the time spent cooling. To answer this, we need to understand at which point the model is designed to be applied.

The initial temperature given by the model when t=0 is 349.2 degrees Celsius. This is where the model starts. As t increases, the temperature decreases. The model is meant to describe cooling from the initial temperature, so it should be most accurate when used to predict times for temperatures less than 349.2 degrees Celsius but above the eventual room temperature where the oven stops cooling down.

Out of the temperatures given (0, 100, 300, 400), the model cannot be most accurate at a temperature higher than 349.2 degrees since the oven did not start above this temperature according to the model. At 0 degrees, this might be significantly away from the model's ideal range if the oven is not supposed to cool down all the way to 0 (as typical room temperature would be higher than 0 degrees Celsius).

Therefore, 300 degrees Celsius is the temperature at which the model will most accurately predict the time spent cooling, as it is within the initial and room temperature range and is within the upper portion of the model’s design.