There is 100 bacteria in a dish after 20 minutes it becomes 10000 how can you turn it into a math equation?

Question

plz i need this by 9:00 pm for school tomorrow

Answer 1

Bacteria grow at an exponential rate.

Every 10 minutes, the bacteria grow by a factor of 10.

x= number of minutes divided by 10

100 * 10^x

Answer 2

Bacteria growth problems are usually represented by the exponential equation

A = Ao[e^(kt)]

where

A = amount of bacteria at any time "t"

Ao = initial amount of bacteria = 100 (given)

k = exponential constant of proportionality

t = time

The above can be rewritten as

A = 100e^(kt)

and since it becomes 1000 after 20 minutes, the above becomes

10000 = 100e^k(20)

100 = e^20k

Taking the natural logarithm of both sides,

ln 100 = 20k (ln e)

Since ln e = 1,

ln 100 = 20k and solving for "k",

k = (1/20)(ln 100)

k = 0.2303

Therefore, the growth equation becomes

A = 100e^(0.2303t) --- this is your formula.

Answer 3

Use the equation:

y = (y0) e^(ct)                  

y0 = the number you started with

10000 = 100e^c(20)          solve for "c"  

divide by 100

take the natural log of both sides ("ln" and "e" cancel on the right)

ln 10000/100 = c(20)      

solve for "c" an then plug it into the initial equation

y = 100e^(__ * t)  

Answer 4

Think about how the bacteria are multiplying. What variable is necessary to complete the equation?

Since you know the initial value, final value, and amount of time involved, the only unknown variable is the rate.

Set up the equation as:

100 (initial value) + rate (unknown)* 20 (time) = 10000 (final value)

This can be rewritten as:

r = (10000-100)/20

Just plug these values into a calculator.