Question

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.

Answer 1

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.

Explanation:

The given linear function is
`y= 9^(5x)` .

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
`y= 9^(5x)` to get the number of days x.

⇒ 243 =
`9^{5x`

• 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
`3^(5)`

⇒
`3^(5)` =
`9^{5x`

⇒
`3^(5)` =
`3^{10x`

⇒ 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