A scientist models the concentration of a chemical in a solution by $C(t)=a\cdot b^t$, where $t$ is measured in hours after the start of an experiment. She records the following data.

At what time $t$ will the concentration first reach $96$?

A small town had a population of $4,000$ in the year 2000. Since then, the population has been modeled by the equation $P=4,000(1.02{)}^t$, where $t$ is the number of years after 2000. According to this model, what is the population when $t=0$?

The graph of $y=a\sqrt{x-1}+4$ passes through the point $(10,10)$. Which expression is equivalent to this function?

The height, in feet, of a ball $t$ seconds after it is dropped is modeled by h=64ig(1-\left(\tfrac{1}{2}\right)^t\big). A sensor is placed so that it turns on when the ball reaches a height of $56$ feet. Which statement must be true about the time when the sensor first turns on?

The area of a square is numerically equal to the length of a rectangle. The width of the rectangle is $4$ units, and the area of the rectangle is $36$ square units. What is the side length of the square, in units?