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fgiga [73]
3 years ago
10

Aliens have injected Ana with mathematical nanobots. These nanobots force Ana to think about math more and more. Initially, ther

e were only five nanobots. The population of the nanobots doubles every hour. The population of the nanobots follows the equations p(t) = 5·2^t. After there are 106nanobots, Ana will cease thinking of anything other than math. How many hours will it take for math to take over Ana's brain?
Mathematics
1 answer:
natulia [17]3 years ago
6 0

Answer:

<em>Math will take over Ana's brain at 4.4 hours</em>

Step-by-step explanation:

<u>Exponential Grow </u>

The population of the nanobots follows the equation  

p(t) = 5\cdot 2^t

We must find the value of t such that the population of nanobots is 106 or more, that is

5\cdot 2^t\geq 106

We'll solve the equation

5\cdot2^t= 106

Dividing by 5

2^t= 106/5=21.2

Taking logarithms

log(2^t)= log(21.2)

By logarithms property

t\cdot log(2)= log(21.2)

Solving for t

\displaystyle t=\frac{log21.2} {log2}

t=4.4 \ hours

Math will take over Ana's brain at 4.4 hours

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