Question

Under ideal conditions a certain bacteria population is known to double every three hours. Suppose that there are initially 70 bacteria.
(a) What is the size of the population after 9 hours?
bacteria

(b) What is the size of the population after t hours?
bacteria

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

Answer 1

a) Double every 3 hours -> 70 *2*2*2 (*2 every 3 hours so 3 times)

Answer 2

Now generalize it for t and use your formula to do part c

Answer 3

okaay thanks you

Answer 4

ur welcome

Answer 5

\[
\text{We can write the population as a function of time as follows.}\\
\ \ \ P(t)=P_02^\frac{t}3\\
\text{where}\\
\ \ \ P(t)\text{ - the population after }t\text{ hours}\\
\ \ \ \ P_0\ \text{ - the initial population}\\
\text{We're given as follows.}\\
\ \ \ P_0=70\\
\text{So we can reduce our function to...}\\
\ \ \ P(t)=70\times2^\frac{t}3\\
\text{a. }P(9)=70\times2^\frac93=70\times2^3=560\\
\text{b. }P(t)=70\times2^\frac{t}3\\
\text{c. }P(16)=70\times2^\frac{16}3\simeq2822
\]

Answer 6

thanks you every much

Answer 7

Estimate the time for the population to reach 20,000. (Round your answer to two decimal places.)

Answer 8

ask oldrin.bataku she will give u answer.....

Answer 9

\[
\text{We need to find }t\text{ such that }P(t)\text{ reaches 20,000.}\\
\ \ \ P(t)=20000\\
\text{Let's try to reduce for }t.\\
\ \ \ 70\times2^\frac{t}3=20000\\
\ \ \ 2^\frac{t}3=\frac{2000}7\\
\ \ \ \frac{t}3=\log_2\frac{2000}7\\
\ \ \ t=3\ \log_2\frac{2000}7\\
\ \ \ \ \simeq24.48\\
\text{Therefore it should take roughly 24.48 hours.}
\]

Answer 10

PS @estudier I'm a boy.

Answer 11

@oldrin.bataku OK, I believe u.....