Final answer:
To find the temperature of the tea after 10 minutes of cooling by 15% per minute from an initial temperature of 85°C, an exponential decay formula is applied, resulting in a temperature of approximately 16.73°C.
Step-by-step explanation:
The student's question pertains to an exponential decay problem in Mathematics, specifically relating to percentage decrease in temperature over time. The temperature of a cup of tea is 85°C and cools by 15% each minute. To find the temperature after 10 minutes, we must apply the exponential decay formula repeatedly or recognize the pattern of decay.
To calculate the temperature after 1 minute we use the formula: T1 = T0 × (1 - decay rate), where T0 is the initial temperature and the decay rate is 15%. Therefore, T1 = 85°C × (1 - 0.15) = 85°C × 0.85 = 72.25°C.
For subsequent minutes, we repeat the process based on the new temperature. After 10 minutes, the formula is: T10 = T0 × (0.85)^10. This results in a temperature of:
T10 = 85°C × (0.85)^10 = 85°C × 0.196874 = 16.73°C (rounded to two decimal places).
Therefore, after 10 minutes, the temperature of the tea would be approximately 16.73°C, assuming that the cooling rate remains constant at 15% per minute.