The online game World of Warcraft has seen a decline in subscribers in recent years. The number of subscribers peaked in 2010 at 11.99 million; in 2015, this number had declined to 5.43 million. Suppose this decline follows the exponential law, and continues uninhibited. If N is the number of subscribers, m millions, and t is the time, in years, since 2010, then: 1. Find a function N that describes this decline.
2. What will the number of subscribers be in 2019?
3. In what year will the number of subscribers fall below 1, 500,000?

Kindly check explanation

Step-by-step explanation:

Given that:

Number of subscribers in 2010 = 11.99 million

Number of subscribers 2015 = 5.43 million

Let :

N = number of subscribers in millions

t = time in years

Exponential function which describes this decline :

N(t) = No×e^kt

Solve for k at t = 5

11,990,000 = 11,990,000 × e^k*0

5,430,000 = 11,990,000 × e^5k

0.4528773 = e^5k

In(0.4528773) = In(e^5k)

−0.792134 = 5k

k = −0.792134 / 5

k = −0.158426

What will the number of subscribers be in 2019?

In 2019

t = (2019 - 2010) = 9

N(t) = 11,990,000×e^(−0.158426*9)

= 11,990,000 * e^(−1.425841)

= 11,990,000 × 0.2403062

= 2,881,511.5 = 2,881,511

3. In what year will the number of subscribers fall below 1, 500,000?

N(t) = No×e^kt

1,500,000 = 11,990,000 × e^(−0.158426*t)

0.1251042 = e^(−0.158426*t)

In(0.1251042) = In(e^(−0.158426*t))

−2.078607 = 0.158426*t

t = (−2.078607 / 0.158426)

t = −13.12036

After 13.12036 years

2010 + 14 = 2024

step-by-step explanation: