Question

It is known that a certain kind of algae in the Dead Sea can double in population every 2 days. Suppose that the population of algae grows exponentially, beginning now with a population of 1,000,000. (a) How long it will take for the population to quadruple in size?

Answer 1

Answer:

4 days

Explanation:

1,000,000*4=4,000,000(total size after quadrupling)

1,000,000*2=2,000,000(after 2 days.)

2,000,000*2=2,000,000(after 4 days.)

therefore it will take 4 days to quadruple in size

Answer 2

It takes four days for the population to quadruple in size.

Given that an exponential function is of the sort;

y = ab^x

Where;

a is the constant, b is the base and x is the exponent.

The population of algae originally present was 1,000,000 and it doubles every two days. If the population quadrupled then we have a population of  4,000,000.

Having these information;

4,000,000 = 1,000,000 (2)^x

(2)^x = 4,000,000/1,000,000

(2)^x = 4

(2)^x = 2^2

If the bases cancel out;

x =2

The time taken for the population to quadruple in size must be  (2)^2 = 4 days.

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