The Euglenae increased exponentially. At first there 1000. Three hours later there were 1,500,000. how many Euglenae would there be at the end of 8 hours?

Question

The Euglenae increased exponentially. at first there 1000. Three hours later there were 1,500,000. How many Euglenae would there be at the end of 8 hours? I assume I just divide 1,400,000 by 3 and then add it 5 times on top of 1,500,000.

Answer 1

The "generic" exponential equation is y = ab^x where "a" is the "starting point" or value when x = zero and "b" is the multiplier. In this case, we are told that "a" = 1000. Then we are given a data point (3, 1500000) so we can plug in that data point to solve for the value of b.

y = ab^x

y = 1000•b^x

1500000 = 1000•b³

1500000/1000 = b³

1500 = b³

b = cuberoot(1500)

b = 11.44714243

So the equation that models this situation is:

y = 1000•(11.44714243)^x

Now, to solve the problem, we need to find "y" when "x" is 8

y = 1000•(11.44714243)⁸

y = 1000•294,833,406.8

y = 2.94833 x 10¹¹ or 294.8 billion