a cup of coffee at 95 degrees Celsius is put into a 25 degree Celsius room when t=0. The coffee's temperature,f(t), is changing at a rate given by f'(t)=-5(0.6)^t degrees Celsius per minute, where t is in minutes. Estimate the coffee's temperature when t=10.

Thank you for taking the time to copy your homework to AMHD.
Please refer to this announcement: https://www.askmehelpdesk.com/financ...-b-u-font.html

Here is one way to go about it.

Newton's Cooling Law says that, in this case:





Integrate and get:



But, at t=0, the coffee is T=95.

Therefore, subbing in T=95 and t=0, we find that C=ln(70).

But, we are also told that



So, we have:



Sub in t=10 and solve for T to find the coffee temp. at t=10.