Question

The number of students using a cell phone application doubles every seven days. The initial number of users is 100. Write an equation for f(t) which represents the number of students who are using the application after t days

Answer 1

Answer:

Following are the solution to the given question:

Step-by-step explanation:

Initial number of users

$N_0=100$ $\text{growth rate=doubles every seven days}$

$100\% \longrightarrow 7\ days\\\\\frac{100}{100} \longrightarrow 7\ days\\\\1 \longrightarrow 7\ days$

When:

$N=N_0\ 2^{rt}$

    $=100\times 2^{rt}\\\\=100\times 2^{t\cdot \frac{1}{7}}\\\\=100\times 2^{ \frac{t}{7}}$

Checking the value:

After 14 days:

$N=100\times 2^{ \frac{14}{7}}=400\\\\100 \overset{100\ days}{\rightarrow} 200 \overset{7 \ days}{\rightarrow}\ 400$