Question

Applications with substitution help. Suppose the rate of change in the temperature of the glass portion of a newly crafted telescope mirror is given by T'(t)= -9e⁻⁰.⁰⁵ᵗ, where T is in Celsius and t is in days since coming out of the furnace. Suppose the temperature of the telescope is initially 1500 C.

What will the temperature be after 30 days? Round to 2 decimals.

Answer 1

To determine the temperature of the telescope mirror after 30 days, integrate the given rate of change function T'(t) and apply the initial condition T(0) = 1500°C.

Step-by-step explanation:

The student is asking about finding the temperature of a telescope mirror after a certain time has passed, given the rate of change of its temperature as a function of time. The rate of change is described by the function T'(t)= -9e⁻⁰.⁰⁵ᵗ, and the initial temperature is 1500°C. To find the temperature after 30 days, one must integrate the rate of change function and apply the initial condition.

To determine the temperature of the telescope mirror after 30 days, integrate the given rate of change function T'(t) and apply the initial condition T(0) = 1500°C.

Integrating T'(t)= -9e⁻⁰.⁰⁵ᵗ, we get the temperature function T(t). The initial condition is that when t=0, T(0)=1500°C. We find T(30) to get the temperature after 30 days and round the result to two decimal places as the student has requested.