Answer
The object is cooling or decreasing at a rate of $7.5^{\circ}/minute$.
Work Step by Step
$T(t) = \frac{3}{8}t^2 - 15t + 180$
To find the rate of change, first we need to find the derivative which we can do using the power rule:
$T'(t) = \frac{3}{4}t - 15$
Now, we substitute t=10 into the equation at that specific point:
$T'(10) = \frac{3}{4}*10 - 15 = 7.5 - 15 = -7.5$
To interpret this data, we note that the rate is negative which implies the temperature goes down or cools down.
So the object is cooling or decreasing at a rate of $7.5^{\circ}/minute$.
