Answer:
2 hours: 3968 <u>[I don't understand the $ sign in the answer box]</u>
At midnight: 12137
Step-by-step explanation:
The bacteria are increasing by 15% every hour. So for every hour we will have what we started with, plus 15% more.
The "15% more" can be represented mathematically with (1 + 0.15) or 1.15. Let's call this the "growth factor" and assign it the variable b. b is (1 + percent increase).
Since this per hour, in 1 hour we'll have (3000)*(1.15) = 3450
At the end of the second hour we're increased by 15% again:
(3450)*(1.15) = 3968.
Each additional hour add another (1.15) factor, If we assign a to be the starting population, this can be represented by:
P = a(1.15)^t for this sample that increase 15% per hour. t is time, in hours.
If a represents the growth factor, and P is the total population, the general expression is
P = ab^t
Using this for a = 3000 and b = 1.15, we can find the total population at midnight after starting at 2PM. That is a 10 hour period, so t = 10
P = (3000)*(1.15)^10
P = 12137
2x - 3y = - 13
the equation of a line in standard form is
Ax + By = C ( A is a positive integer and B, C are integers )
First obtain the equation in slope-intercept form
y = mx + c ( m is the slope and c the y-intercept )
calculate m using the gradient formula
m = ( y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (1, 5 ) and (x₂, y₂ ) = (- 2, 3 )
m = 
= 
= 
y = x + c ← partial equation
to find c substitute either of the 2 points into the partial equation
using (1, 5 ), then
5 = + c ⇒ c = 
rearrange the equation into standard form
multiply through by 3
3y = 2x + 13 ( subtract 3y and 13 from both sides )
2x - 3y = - 13 ← in standard form
Step-by-step explanation:
Sam, Raj and Jade have 12 sweets each
(one person has 12 sweets)
Sam has 12 sweets
one quarter of Sam sweet is blue
1/4 = one quarter
1/4 * 12 = 3
Sam has 3 blue sweets.
4x+16=6x
16=2x
8=x
And 11y+6x=180 (line)
11y+6(8)=180
11y+48=180
11y=132
Y=12
