Humicide algebra problem (help)

Question

A coroner arrives on the scene of a homicide at 8:00 pm in a temperature-controlled room, held at 60 degrees F. The temperature of the body is given by the function 𝑇(𝑡) = 28.6𝑒^-0.0008t + 60, where 𝑡 is time in minutes since 8:00 pm.

a. Graph this function in an appropriate window.

1. What happens to this function as time goes by? Why does this make sense?
2. Use the graph to approximate the time of death, assuming that normal body temperature is 98.6 degrees F.

Answer 1

1) We can rewrite the equation as 60 + 28.6/e^0.0008t. the constant part of the equation, 60, doesn't change as t increases. Therefore, we need to look at the variable part of the equation (28.6/e^0.0008t). As we can see, the larger t becomes (the more minutes go by) the larger the denominator becomes (decreasing the size of the number), which means that the total temperature must be decreasing. This makes sense because a dead person's body temperature is going to decrease from 98.6 deg F to room temperature since his body is no longer creating heat (due to being dead).

Also, we can see that the variable part of the equation (28.6/e^0.0008t) is becoming smaller at an exponential rate (the denominator is increasing exponentially). therefore, the function should look like a decreasing exponential function.

2) You should see the answer on your graphing calculator.