A bacteria cell splits into two cells every hour. Write and evaluate an exponential expression to find how many cells there will be in six hours. Then use your answers to help you find the number of hours it will take for there to be 1024 cells.

easy

equation is
f(x)=2ˣ

where x=number of hours elapsed

after 6 hours
f(6)=2⁶=64 bacteria

to solve for 1024

1024=2ˣ
take ln of both sides
ln(1024)=ln(2ˣ)
ln(1024)=x(ln(2))
divide both sides by ln(2)
ln(1024)/ln(2)=x
using calculator
10=x

or you could recognize that
1024=2¹⁰
or keep divising 1024 by 2

10 hours for 1024 bacteria

Answer Link

xero099 xero099 · Answer 2 · 2021-08-13T22:00:54+02:00

The bacteria will take 10 hours to be 1024 bacteria.

This example of the bacteria is a case of Exponential Progression, which multiplies itself at a constant rate. This kind of progression is defined by the following expression:

[tex]n = n_{o}\cdot r^{t}[/tex] (1)

Where:

[tex]n_{o}[/tex] - Initial population of the bacteria, no unit.

[tex]n[/tex] - Current population of the bacteria, no unit.

[tex]r[/tex] - Increase rate, no unit.

[tex]t[/tex] - Time, in hours.

Then, if we know that [tex]n_{o} = 1[/tex], [tex]r = 2[/tex] and [tex]n = 1024[/tex], then the time taken by the bacteria is:

[tex]\frac{n}{n_{o}} = r^{t}[/tex]

[tex]\log \frac{n}{n_{o}} = t\cdot \log r[/tex]

[tex]\log n - \log n_{o} = t\cdot \log r[/tex]

[tex]t = \frac{\log n - \log n_{o}}{\log r}[/tex]

[tex]t = \frac{\log 1024-\log 1}{\log 2}[/tex]

[tex]t = 10\,h[/tex]

The bacteria will take 10 hours to be 1024 bacteria.

Please see this question related to Exponential Progression: https://brainly.com/question/4853032