Current Attempt in Progress Let t be the number of years since farming began in a region . The number, N, of acres of harvested land at time tis given by N=f(t)=150sqrt (t) Find f(25)cdot f'(25) and the relative rate of change (f')/(f) at t=25. Interpret your answers in terms of harvested land. Enter exact answers. f(25)=boxed (1) f'(25)=boxed (1) (f'(25))/(f(25))=boxed (1)

## Step 1<br />The problem provides a function \(N=f(t)=150\sqrt{t}\), which represents the number of acres of harvested land at time \(t\). We are asked to find the values of \(f(25)\), \(f'(25)\), and the relative rate of change \(\frac{f'}{f}\) at \(t=25\).<br /><br />## Step 2<br />First, we need to find the value of \(f(25)\). This is done by substituting \(t=25\) into the function \(f(t)\).<br /><br />### \(f(25)=150\sqrt{25}\)<br /><br />## Step 3<br />Next, we need to find the derivative of \(f(t)\), which is \(f'(t)\). The derivative of a function gives us the rate of change of the function at any given point.<br /><br />### \(f'(t)=\frac{150}{2\sqrt{t}}\)<br /><br />## Step 4<br />Now, we substitute \(t=25\) into \(f'(t)\) to find \(f'(25)\).<br /><br />### \(f'(25)=\frac{150}{2\sqrt{25}}\)<br /><br />## Step 5<br />Finally, we calculate the relative rate of change \(\frac{f'}{f}\) at \(t=25\).<br /><br />### \(\frac{f'(25)}{f(25)}=\frac{\frac{150}{2\sqrt{25}}}{150\sqrt{25}}\)