Question

A lake has been infected by some type of new algae that is unknown. Every single day the amount of surface area that the algae takes up doubles. Day 1 has a certain amount, day 2 it is 2x that amount. It takes 87 days for the entire lake to be overrun by this new algae. How many days does it take to cover half of the lake? Show your work and explain your thinking. In science we need to be able to justify our answers.

hint: It is not the "obvious" answer.

Answer 1

It takes 86 days take to cover half of the lake

Step-by-step explanation:

In the day #1, the amount of the algae is X,

In the day #2 is 2X

In the day #3 is 2*2*X = X*2²

...

In the day #n the amount of the algae is X*2^(n-1)

Assuming X = 1m³. In the day 87, the area infected was:

1m³*2^(87-1)

7.74x10²⁵m³ is the total area of the lake

the half of this amount is 3.87x10²⁵m³

The time transcurred is:

3.87x10²⁵m³ = 1m³*2^(n-1)

Multiplying for 5 in each side:

ln (3.87x10²⁵) = ln (2^(n-1))

58.9175 = n-1 * 0.6931

85 = n-1

86 = n

It takes 86 days take to cover half of the lake