Answer:
B. Only the monthly rental cost of apartments in Lowell is changing exponentially.
Step-by-step explanation:
To identify how the values of the monthly costs of the departments are changing, we must do a test.
The test consists of taking an element [tex]n_{-1}[/tex] and the element n of the series, and dividing [tex]\frac{n}{n_{-1}} = a[/tex]
Then take the element [tex]n_{+1}[/tex] and the element n and divide [tex]\frac{n_{+1}}{n} = b[/tex]
If b = a, then the exponential function of base "b"
But if b> a, then the rate of change of the function is not exponential
For example. For the cost of apartments in Beverly
[tex]n_{-1} = 1870\\n = 1890\\n_{+1} = 1950\\\\\frac{n}{n_{-1}} = \frac{1890}{1870} = 1.011\\\\\frac{n_{+1}}{n} = \frac{1950}{1890} = 1.032\\\\1,032> 1,011[/tex]
So, the cost of apartments in Beverly does not increase at an exponential rate.
We do the same for the cost of the apartments in Lowell.
[tex]n_{-1} = 1600\\n = 1680\\n_{+1} = 1764\\\\\frac{n}{n_{-1}} = \frac{1680}{1600} = 1.05\\\\\frac{n_{+1}}{n} = \frac{1764}{1680} = 1.05\\\\1.05 = 1.05[/tex]
The rate is the same, so the prices increase exponentially.
Finally, the correct answer is option B: B. Only the monthly rental cost of apartments in Lowell is changing exponentially.
