### Part 1:

The position of the ant as a function of time, t minutes, can be modeled with the equation $f(t)=150(0.75)^{t}$
Notice that decreasing by $25 \%$ of the distance means “keeping” $75 \%$ of the distance.
Complete the table for various times. Round your answers to $3$ decimal places.
 Time $t$ (minutes) Position $f(t)$ (inches) $0$ $10$ $20$ $40$
Notice that even at $t=40$ the answer is small, but it is not zero.
In fact, there is no way to actually get to zero. No matter how much time goes by, $25 \%$ of any non-zero number is always non-zero. The ant will never get to the wall!

Solution: