Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that there are initially 70 bacteria.

AWhat is the size of the population after 9 hours?

bacteria

BWhat is the size of the population after t hours?

bacteria

CWhat is the size of the population after 16 hours? (Round your answer to the nearest whole number.)

just keep squaring the number. 70 x 2 = 140 after 1 hour
140 x 2 = 280 after 2 hours
280 x 2 = 560 bacteria after 3 hours.
Bacteria = initial amount times hours times 2
B=ih2

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misscaffeine misscaffeine · Answer 2 · 2016-09-13T09:28:27-04:00

To resolve this problem you need the following equation for exponential growth: \(N(t) = N_{0} e^{rt}\).

The N(t) represents the size of the population in a concrete moment of time (t), the N_{0} is the initial size of the population and the rt refers to the rate of growth of said population. Baring this in mind, here are the answers:

a) N(9) = 70 × 2³ = 560

b)

N(t) = 70 × 2^{t/3}

So let's say the number of bacteria is 120000

1200000 = 70 × 22^{t/3}
1200000 ÷ 70 = 22^{t/3}
17142.9 = 22^{t/3}
log_2 17142.8 = log_2 22^{t/3}
14.07 = t/3
t = 14.07×3
t = 42.21

c) N(16) = 70 × 2^{16/3} = 1529173.3333333333333333 = 1529173