Applications of Integration — Quiz 4

Questions in this quiz (5)

1. A cup of coffee at $$180^\circ$$F is placed in a room whose temperature is $$60^\circ$$F. The temperature of the coffee is cooling at time $$t$$ at the rate$$R(t)=-8e^{-0.06t}$$ $$^\circ$$F per minute. The temperature, to the nearest degree $$^\circ$$F, of the coffee $$15$$ minutes after it is placed in the room is:

   • $$95^\circ$$
   • $$101^\circ$$
   • $$108^\circ$$
   • $$115^\circ$$

2. What is the total area bounded by the curve$$f(x)=x^3-3x^2-4x$$ and the $$x$$-axis on the interval $$0\le x\le4$$?

   • $$2.67$$
   • $$4$$
   • $$5.33$$
   • $$32.00$$

3. An observer recorded the velocity of an object moving along the $$x$$-axis for $$12$$ seconds. Based on the table below, use a trapezoidal approximation, with $$5$$ subintervals indicated in the table, to estimate how far from its starting point the object is at the end of this time.

   • $$2$$ units
   • $$4$$ units
   • $$5$$ units
   • $$7$$ units

4. If a factory continuously releases chemicals into a river at the rate$$P(t)=\frac{\sqrt{t}}{150}$$ tons per day, where $$t$$ is measured in days, then the total amount released after $$5$$ weeks is approximately:

   • $$0.63$$ ton
   • $$0.88$$ ton
   • $$0.92$$ tons
   • $$1.27$$ tons

5. A mobile app launched at $$10$$ A.M., and the rate of downloads, measured in downloads per hour, increased continuously during the first $$6$$ hours. The graph of $$R(t)$$, the rate of downloads for the app in downloads per hour, is shown below, where $$t$$ is the number of hours since the app launched. Using a midpoint or trapezoidal sum, approximate the time when the $$500$$th download occurred.

   • between $$11$$ A.M. and $$12$$ P.M.
   • between $$12$$ P.M. and $$1$$ P.M.
   • between $$1$$ P.M. and $$2$$ P.M.
   • after $$2$$ P.M.