a. A city is in the shape of a rectangle. In 2015 the width of the city was4 miles and the length of the city was3miles. The width of the city is growing at a rate of1 mile in5years. The length of the city is growing at a rate of1mile in5 years. Use the product rule to find how quickly the area of the city is growing in 2015.

_____________ square miles per year

b. A tree trunk is approximated by a circular cylinder of height50 meters and diameter4 meters. The tree is growing taller at a rate of1 meters per year and the diameter is increasing at a rate of5 cm per year. The density of the wood is5000kg per cubic meter.How quickly is the mass of the tree increasing? ______________kilograms per year

c .A rectangle initially has width4 meters and length3meters and is expanding so that the area increases at a rate of2square meters per hour. If the width increases by30centimeters per hour, how quickly does the length increase initially?Hint: Using the product rule, if you know any two of the derivatives you can work out the third one. Here you know=, A', and W'.

The length is increasing at______________centimeters per hour