A town installs a new sound-monitoring device near a highway. The average sound level, in decibels, at a distance of $d$ meters from the highway is modeled by $S(d)=96-20{\log }_{10}(d)$. A neighborhood rule requires the sound level to be no more than the square root of $4096$ decibels. What is the least whole number of meters from the highway where the device can be placed to meet the rule?

A scientist models the brightness of a certain light source with the equation $B=3^t$, where $t$ is the time in seconds after the source is turned on. She also models a sensor reading with the equation $B=\sqrt{81x}$, where $x$ is a positive constant. If the sensor reading and the brightness are equal when $t=2$, what is the value of $x$?

For $x>0$ and $x\ne 1$, which expression is equivalent to

The table shows several points on the graph of the equation $y=\sqrt{x+k}$, where $k$ is a constant.

What is the value of $k$?

A biologist places a culture of bacteria into a dish. The number of bacteria in the dish can be modeled by N(t)=500ig(2^{t/3}ig), where $t$ is the number of hours since the culture was placed in the dish. According to the model, after about how many hours will the dish contain $4,000$ bacteria?