Final answer:
To calculate the time taken for the temperature to drop to 25°C, set T(t) equal to 25, solve for t by taking the natural logarithm of both sides, and then divide by ln(0.913).
Step-by-step explanation:
To find the time taken for the temperature of the dish to fall to 25°C from 80°C when removed from the microwave, we use the provided temperature function T(t)=80 × (0.913)^t and set it equal to 25°C. So, the equation to solve is 25 = 80 × (0.913)^t. Taking the natural logarithm on both sides gives us ln(25/80) = t × ln(0.913).
To isolate the variable t, we then divide by ln(0.913), which gives t = ln(25/80) / ln(0.913). Solving this equation with a calculator will give the desired time in minutes.
To find the time taken for the temperature of the dish to fall to 25°C, we need to set T(t) equal to 25 and solve for t. So, we have the equation 25 = 80 x (0.913)t. To solve for t, we can take the logarithm of both sides. Using logarithmic properties, we get t = log(25/80)/log(0.913). Using a calculator, we can find that t ≈ 13.04 minutes.