To transform the function
to have the amplitude of 3, we need to multiply the constant 3 to the function f(x), so we have
To transform the function
to have the midline
we need to subtract
by 4, so we have
,
To transform the function
to have period of
, we need to divide the original period
by 4, so we have
. Note that it is the
gives the effect of dividing the points on x-axes by 4 and the period is read on x-axes
Hence, the full transformation is given
which is the last option
Answer:
The time it will take the population to grow to 800 insects is 17 days.
Step-by-step explanation:
The growth function of the insects is exponential.
The exponential growth function is:
Here,
<em>y</em> = final value
<em>a</em> = initial value
<em>r</em> = growth rate
<em>t</em> = time taken
It is provided that there were 270 insects after 9 days and initially there were 80 insects.
Compute the value of <em>r</em> as follows:
Now, compute the time it will take the population to grow to 800 insects as follows:
Thus, the time it will take the population to grow to 800 insects is 17 days.
Answer:
When x = 4, (4, 0)
When y = 4, (6, 4)
Step-by-step explanation:
To find the ordered-pair solution when x = 4, plug 4 into the x of the equation.
y = 2x - 8
y = 2(4) - 8
y = 8 - 8
y = 0
This produces the ordered pair (4, 0).
To find the ordered-pair solution when y = 4, plug 4 into the y of the equation.
y = 2x - 8
4 = 2x - 8
12 = 2x
6 = x
x = 6
This produces the ordered pair (6, 4).
Answer:
- y = 0.937976x +12.765
- $12,765
- $31,524
- the cost increase each year
Step-by-step explanation:
1. For this sort of question a graphing calculator or spreadsheet are suitable tools. The attached shows the linear regression line to have the equation ...
... y = 0.937976x + 12.765
where x is years since 2000, and y is average tuition cost in thousands.
2. The y-intercept is the year-2000 tuition: $12,765.
3. Evaluating the formula for x=20 gives y ≈ 31.524, so the year-2020 tuition is expected to be $31,524.
4. The slope is the rate of change of tuition with respect to number of years. It is the average increase per year (in thousands). It amounts to about $938 per year.
5. [not a math question]
Answer:
speed = 
Step-by-step explanation:
using the formula that relates distance/ speed/ time
distance = speed × time
hence speed = 
=
