Question

The temperature, t, in degrees celsius, in a warehouse changes according to the function t(h) = 18 + 4sin(pi/12 (x = 8)).

where h is the number of hours since midnight. at what rate is the temperature changing at 9 a.m.?

Answer 1

about 1.01 °C per hour

Explanation:

We assume the intended temperature function is ...

t(h) = 18 +4·sin(π/12(h -8))

We are asked for the rate of change when h=9.

__

derivative

The rate of change of temperature with respect to time is the derivative of t(h) with respect to h.

t'(h) = 4(π/12)cos(π/12(h -8)) = π/3·cos(π/12(h -8))

at 9 am

For h = 9 hours after midnight, the rate of change is ...

t'(9) = π/3·cos(π/12(9 -8)) = π/3·cos(π/12) ≈ (3.14159)(0.965926)/3

t'(9) ≈ 1.01152

The rate of change of temperature at 9 a.m. is about 1.01 °C/hour.