## Calculus with Applications (10th Edition)

$D(q)=-0.4q+6.9$
The function is $p=S(q)=0.3q+2.7$ with $D(2)=6.1$ which is also $(q_2,p_2)=(2,6.1)$ To find the quantity demanded at a price of $\$4.50$per watermelon, replace p in the demand function with$4.50$and solve for q.$4.50=0.3q+2.70.3q=1.8q=6$To find m we use the formula:$m=\frac{p_2-p_1}{q_2-q_1}=\frac{6.1-4.5}{2-6}=-\frac{4}{5}=-0.4$Assume that the demand function is linear, we have$p-p_1=m(q-q_1)D(q)-4.5=-0.4(q-q_1)D(q)-4.5=-0.4q+2.4D(q)=-0.4q+6.9\$