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1 answer:
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Given:
The inequality is:
To find:
The y-intercept, slope and type of line (solid or dotted).
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope and b is the y-intercept.
We have,
The relation equation is:
...(ii)
On comparing (i) and (ii), we get
It means the slope is 5 and the y-intercept is 3.
The sign of the inequality in the given inequality is ">". It means the boundary line is not included in the solution set. So, the boundary line is a dotted line.
Therefore, the slope is 5, the y-intercept is 3 and the line is a dotted line.
Answer:
The number of bacteria in the dish after 9.9 minutes is 478
Step-by-step explanation:
The form of the function is , where a is the initial amount (value f(x) at x = 0)
To find a and b let us use two points from the graph and substitute their coordinates in the equation
∵ The graph passes through point (1 , 1)
∴ x = 1 and y = 1
- Substitute them in the equation
∵
∴ a.b = 1 ⇒ (1)
∵ The graph passes through point (1 , 1)
∴ x = 3 and y = 4
- Substitute them in the equation
∵
∴ a.b³ = 4 ⇒ (2)
Use equation (1) to find a in terms of b
∵ a.b = 1
- Divide both sides by b
∴ ⇒ (3)
- Substitute a in equation (2) by equation (3)
∴ . b³ = 4
- Remember the rule
∵ . b³ =
= b²
∴ b² = 4
- Take √ for both sides
∴ b = 2
Substitute the value of b in equation (3) to find a
∵ a =
∴ a = 0.5
∴
∵ f(x) represents the number of bacteria after x minutes
∵ x = 9.9 minutes
- Substitute x by 9.9 to find the number of bacteria
∵
∴ f(9.9) = 477.7128917
- Round it to the nearest whole number
∴ f(9.9) = 478
∴ The number of bacteria in the dish after 9.9 minutes is 478