Question

Samuel compared the monthly rental rates of two-bedroom apartments in Beverly and Lowell over the years. The results are shown in the table below. Time (years) Beverly Rent ($) Lowell Rent ($) 0 1,870 1,600 1 1,890 1,680 2 1,950 1,764 3 2,055.50 1,852.20 4 2,175.75 1,944.81 Which statement best describes this situation? A. Only the monthly rental cost of apartments in Beverly is changing exponentially. B. Only the monthly rental cost of apartments in Lowell is changing exponentially. C. The monthly rental cost of apartments in neither town is changing exponentially. D. The monthly rental cost of apartments in both the towns is changing exponentially.

Answer 1

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 $n_{-1}$ and the element n of the series, and dividing $\frac{n}{n_{-1}} = a$

Then take the element $n_{+1}$ and the element n and divide $\frac{n_{+1}}{n} = b$

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

$n_{-1} = 1870\\n = 1890\\n_{+1} = 1950\\\\\frac{n}{n_{-1}} = \frac{1890}{1870} = 1.011\\\\\frac{n_{+1}}{n} = \frac{1950}{1890} = 1.032\\\\1,032> 1,011$

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.

$n_{-1} = 1600\\n = 1680\\n_{+1} = 1764\\\\\frac{n}{n_{-1}} = \frac{1680}{1600} = 1.05\\\\\frac{n_{+1}}{n} = \frac{1764}{1680} = 1.05\\\\1.05 = 1.05$

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.