Question

A cell phone tower has a safety light to warn airplanes of its location. It blinks once every 3.5 seconds. If f(m) gives the number of times the light blinks over the course of m minutes, which of the following equations defines f

• A. $f\left(m\right)=2.5m$
• B. $f\left(m\right)=\frac{3.5m}{60}$
• C. $f\left(m\right)=\frac{60m}{3.5}$
• D. $f\left(m\right)=210m$

Answer 1

The correct option is C $f\left(m\right)=\frac{60m}{3.5}$

Cell phone tower blinks after every $3.5$ seconds i.e after every $\frac{3.5}{60}$minutes (1min=60sec).

Thus f(m) gives number of times light blinks after m minutes.

For first blink ,it takes $\frac{3.5}{60}$ minutes

For Second blink, it takes $\frac{3.5}{60}$+$\frac{3.5}{60}$ minutes

i.e $\frac{2\times 3.5}{60}$

For Third blink it takes $\frac{3.5}{60}$+$\frac{3.5}{60}$+$\frac{3.5}{60}$ minutes i.e $\frac{3\times 3.5}{60}$

So for $t$ blinks, it take over a course of $\frac{t\times 3.5}{60}$ minutes

We need to find over given m minutes, how many times it will blink which will be given by total time divided by time taken for one blink.

So over a course of time $m$ minutes it will blink $\frac{m}{\frac{3.5}{60}}=\frac{60m}{3.5}$