$1 \leftarrow \quad$ A garden shop determines the demand function $q=D(x)=\frac{4 x+300}{10 x+13}$ during early summer for tomato plants where $q$ is the number of plants sold per day when the price is $x$ dollars per plant. (a) Find the elasticity. (b) Find the elasticity when $x=2$. (c) At $\$ 2$ per plant, will a small increase in price cause the total revenue to increase or decrease?

Step 1 ：Given the demand function \(D(x)=\frac{4x+300}{10x+13}\), where \(q\) is the number of plants sold per day when the price is \(x\) dollars per plant.

Step 2 ：The elasticity of demand is a measure of how much the quantity demanded of a good responds to a change in the price of that good. It is calculated as the percentage change in quantity demanded divided by the percentage change in price.

Step 3 ：To find the elasticity, we first need to find the derivative of the demand function with respect to price, and then multiply that by the ratio of price to quantity. The derivative of the demand function is \(-10\frac{4x+300}{(10x+13)^2} + \frac{4}{10x+13}\).

Step 4 ：The elasticity of demand is then given by the expression \(E = x\frac{(10x+13)(10(4x+300)/(10x+13)^2 - 4/(10x+13))}{4x+300}\).

Step 5 ：To find the elasticity when \(x=2\), we substitute \(x=2\) into the elasticity expression to get \(E = \frac{134}{231}\).

Step 6 ：Final Answer: The elasticity when \(x=2\) is \(\boxed{\frac{134}{231}}\).