Answer:
The insect population after 6 days is of 1639 insects.
Step-by-step explanation:
A population of insects increases at a rate 230 + 8t + 0.9t2 insects per day
This means that
The population of insects after x days is given by:
So
In which K is the initital population(which is 50). So
After 6 days:
Rounding to the nearest insect, 1639
The insect population after 6 days is of 1639 insects.
All you need to know is that
So, the first function grows exponentially and the second decays exponentially. The rate of growth/decay are the bases of the exponentials, which means 1.08 and 0.205
Answer:
y = - 4x + 13
Step-by-step explanation:
In order to do this problem you would need a whole new equation, but you will use what is given to you:
instead of going with:
x - 4y = 20
Turn it into y = mx + b form, also known as slope-intercept form:
x - 4y = 20
-x = -x
_________
- 4y = 20 - x
Then divide both sides by - 4:
You will then get:
y =
From this equation we will only need the slope!
m || =
(This slope is for parallel)
but if you want perpendicular to the slope, then we need the negative reciprocal!
Negative reciprocal is a flipped version of the value that is negative, for example:
2 =
Because = 2
Now we will find the perpendicular slope which is:
m ⊥ = - 4
Now substitute this slope into slope intercept form:
y = mx + b
(-3) = -4(4) + b
(Take away parentheses)
-3 = -16 + b
(Move - 3 to the other side, by making it positive, but what you do to one side, you do to the other)
= -13 + 6
(Move - 13 to the other side, by make - 13 into +13)
+13 = +13
________
13 = b
(This is you b, also known as you intercept)
Your answer is:
y = -4x + 13