Question

Bacteria in a pond multiplies as shown in the table. If a fungus on a tree decays at half that rate, what is the rate of decay (round to the nearest integer)?

thanks!

Answer 1

20%

Explanation:

Population growth formula:

`P = P_0 * e^(rt)`

where P is the total population after time t,
`P_0</p><p>` is the starting population, r is the rate of growth and t is the time in hours

Solving for r:

`(ln((P)/(P_0)))/(t)=r`

and replacing with data:

P = 22.781

`P_0` = 4.5 (taking hour 2 as initial time)

t = 4 hours (time elapsed between initial time and time the population reach P)

r = 0.4, that is equivalent to 40%

Then, fungus decay rate is 40%/2 = 20%

Answer 2

Using the formula, y=a(1=r)^x to solve for the growth rate and you find that the growth rate for the bacteria is 50%. Once this information is found, you can determine that a fungus decay at half that rate will be 25%.