Check 4,5,6and3 please
1 answer:
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Answer:
The monthly growth rate is 3.5%.
Step-by-step explanation:
The exponential growth function is given as follows:
Here,
<em>y</em> = final value
<em>a</em> = initial value
<em>r</em> = growth rate
<em>x</em> = time taken
The provided expression for the monthly growth of membership in the new drama club at a school is:
Comparing this function with the exponential growth function:
Then value of <em>r</em> is 0.035 or 3.5%.
Thus, the monthly growth rate is 3.5%.
Answer:
Vertex is (-4, -18)
Step-by-step explanation:
f(x) =
Let (h, k) be the vertex
An easy way to find h is to use the formula h = -b/2a
In your case where f(x) = a = 2 and b = 8
So, h = -8/2(1) = -8/2 = -4
Substitue -4 in for x to find k
k = () + 8(-4) - 2
= (16) - 32 - 2
= 16 - 32 - 2
= -18
Vertex is (-4, -18)
Note: Another way to find the vertex is to complete the square, but this can really be difficult in some cases
To find f'(3) (f prime of 3), you must find f' first. f' is the derivative of the function f(x).
Finding the derivative of f(x) = 2x⁴ requires the use of the power rule.
The power rule for derivatives is . In other words, you bring the exponent forward and multiply it by the coefficient of the term, and then you subtract 1 from the original exponent.
f'(x) = (2x⁴)
f'(x) = 2(4)x³
f'(x) = 8x³
Now, to find f'(3), plug 3 into your derivative.
f'(3) = 8(3)³
f'(3) = 216
<h3>Answer:</h3>f'(3) = 216