Exponential Growth

Question

1. A super-deadly strain of bacteria is causing the zombie population to double every 2 days. Currently, there are 25 zombies. After how many days will there be 25,600 zombies?
2. Use the function from the previous question. If the current population of our planet is 5,000,000,000 people, after how many days will there be no humans left?

Answer 1

25600 = 25(2)^t/2

1024 = 2^t/2

2¹⁰ = 2^t/2

10 = t/2

20 = t

In 20 days there shall be 25600 Zombies.

50 x 10⁸ = 25(2)^t/2

2 x 10⁸ = 2^t/2

log (2 x 10⁸) = (t/2)(log 2)

log 2 + 8 = (t/2) log 2

0.3010 + 8 = (t/2)(0.3010)

8.3010 = (t/2)(0.3010)

16.6020 = 0.3010t

55.2 = t

On the 56th day humanity ceases.