Question

Rachel has a large pond on her property. The pond contains many different kinds of fish including bass. She knows that the population of the bass is increasing exponentially each year at a rate of 4.8%. She also knows that there are currently between 250 and 275 bass in the pond.
If P represents the actual population of the bass in the pond and t represents the elapsed time in years, then which of the following systems of inequalities can be used to determine the possible number of bass in the pond over time?

Answer 1

The correct choice is the third one,
$\left \{ {{P \geq 250e^{0.048t}} \atop {P \leq 275e^{0.048t}}} \right.$

These inequalities will be based on the equation 
$A=p*e^{rt}$, where A is the total amount, p is the initial population, r is the growth rate as a decimal number, and t is the amount of time.  For our problem, r = 4.8% = 4.8/100 = 0.048.

However, we have two possible initial amounts; 250, the lower end, or 275, the upper end.  Since the lowest the current population can be is 250, this means that our value will be greater than or equal to this.

The other end of our current population estimate is 275.  This means that our value must be less than or equal to this.

Answer 2

Answer:

look at the picture(: