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In a laboratory experiment, the population of bacteria in a petri dish started off at
2600 and is growing exponentially at 13% per day. Write a function to represent the
population of bacteria after t days, where the hourly rate of change can be found
from a constant in the function. Round all coefficients in the function to four decimal
places. Also, determine the percentage rate of change per hour, to the nearest
hundredth of a percent.

In a laboratory experiment the population of bacteria in a petri dish started off at 2600 and is growing exponentially at 13 per day Write a function to represe class=

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mhanifa

Answer:

  • See below

Step-by-step explanation:

Daily growth rate is 13% with initial values of 2600 bacteria.

The equation is:

  • [tex]f(t) = 2600*( 1 + 0.13)^t=2600*1.13^t[/tex]

Find the hourly rate x considering 1 day = 24 hours:

  • [tex]2600*1.13^{t/24}=2600*x^t[/tex]
  • [tex]ln 1.13^{t/24}=ln x^t[/tex]
  • [tex]ln1.13^{1/24}=lnx[/tex]
  • [tex]x=1.13^{1/24} =1.0051[/tex]

Percentage rate of change per hour is:

  • 0.51%

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