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The size of bacteria colony, y, in millions of cells, after x days, is represented by the following function: y=9^5x



The number of days to reach a count of 243 million can be found by solving the linear equation ___x = ___
.

It will take bacteria___ day(s) to reach a count of 243 million.

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It takes half a day for the bacteria to reach 243 million. The linear equation is solved for x= 0.5 or x=1/2.

Step-by-step explanation:

The given linear function is  [tex]y= 9^{5x}[/tex] .

where,

  • 'y' represents the size of bacteria in millions.
  • 'x' represents the number of days to reach the size.

To find the number of days to reach the size of 243 million :

  • The linear equation must be solved for y,
  • It is given that the size of bacteria, y= 243.

Substitute y=243 in the linear equation [tex]y= 9^{5x}[/tex] to get the number of days x.

⇒ 243 = [tex]9^{5x[/tex]

  • To find x, bring the base number as 9 in both sides to equal the exponents.
  • For that, the number 243 must be split into 9×9×3 = 243
  • Again bringing the base number as 3 in both sided to equate the exponents.

⇒ 243 can also be written as [tex]3^{5}[/tex]

⇒ [tex]3^{5}[/tex] =  [tex]9^{5x[/tex]

⇒  [tex]3^{5}[/tex] =  [tex]3^{10x[/tex]

⇒ The powers in both sides are 5 and 10x . The bases in both sides are same.

⇒ Comparing the power on both sides to solve for x value.

⇒ 10x = 5

⇒ x = 5/10

x= 1/2

x= 0.5

It takes half a day for the bacteria to reach 243 million

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