How does f(t)=7^t change over the interval from t=5 to t=6 f(t) increases by 7% f(t) increases by 600% f(t) decreases by 7% f(t) increases by 7

To determine how the function \( f(t) = 7^t \) changes over the interval from \( t = 5 \) to \( t = 6 \), we need to calculate the values of \( f(t) \) at these points and then find the percentage change.<br /><br />First, calculate \( f(5) \):<br />\[ f(5) = 7^5 \]<br /><br />Next, calculate \( f(6) \):<br />\[ f(6) = 7^6 \]<br /><br />Now, find the percentage increase from \( t = 5 \) to \( t = 6 \):<br />\[ \text{Percentage Increase} = \left( \frac{f(6) - f(5)}{f(5)} \right) \times 100\% \]<br /><br />Let's compute these values step-by-step:<br /><br />1. Calculate \( 7^5 \):<br />\[ 7^5 = 16807 \]<br /><br />2. Calculate \( 7^6 \):<br />\[ 7^6 = 117649 \]<br /><br />3. Calculate the percentage increase:<br />\[ \text{Percentage Increase} = \left( \frac{117649 - 16807}{16807} \right) \times 100\% \]<br />\[ \text{Percentage Increase} = \left( \frac{100942}{16807} \right) \times 100\% \]<br />\[ \text{Percentage Increase} \approx 600\% \]<br /><br />Therefore, the correct answer is:<br />\[ f(t) \text{ increases by } 600\% \]