The population of a fast-growing city in Texas can be modeled with the equation . The population of a fast-growing city in Tennessee can be modeled with . In both equations, represents years since 2016, and the population is measured in thousands. The graphs representing the two functions are shown. The point where the two graphs intersect has a -coordinate of about 271.7.

1. What does the intersection mean in this situation?
2. Find the -coordinate of the intersection point by solving each equation. Show your reasoning.
3. Explain why we can find out the value at the intersection of the two graphs by solving .

The function is given by . Select all equations whose graph meets the graph of for a positive value of .

The half-life of nickel-63 is 100 years. A student says, “An artifact with nickel-63 in it will lose a quarter of that substance in 50 years.”

Do you agree with this statement? Explain your reasoning.

Technology required. Estimate the value of each expression and record it. Then use a calculator to find its value and record it.

Here is a graph that represents . 

Explain how we can use the graph to estimate:

1. the solution to an equation such as .
2. the value of .