Answer:
ANSWER:
An exponential growth function has constant doubling time.
Step-by-step explanation:
EXPLANATION:
The formula for calculating exponential growth is
A=A'e^kt
here:
A=amount after growth
A'=initial value
e=2.718
k=continuous growth rate
t=time passed
Answer:
Direction is missing
Step-by-step explanation:
Veronica’s velocity was measured as 4.3 m/s. She displaced 20 meters in 4.7 seconds. We know that velocity is a vector quantity. It has both magnitude as well as direction. Velocity is defined as the total distance per unit time I.e.
i.e. the magnitude of velocity is 4.3 m/s
Here, only velocity is given but its direction is missing. So, the missing information is " the direction ".
![\bf f(x)=(x-6)e^{-3x}\\\\ -----------------------------\\\\ \cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)] \\\\\\ \cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}](https://tex.z-dn.net/?f=%5Cbf%20f%28x%29%3D%28x-6%29e%5E%7B-3x%7D%5C%5C%5C%5C%0A-----------------------------%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3D1%5Ccdot%20e%5E%7B-3x%7D%2B%28x-6%29-3e%5E%7B-3x%7D%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%5B1-3%28x-6%29%5D%0A%5C%5C%5C%5C%5C%5C%0A%5Ccfrac%7Bdy%7D%7Bdx%7D%3De%5E%7B-3x%7D%2819-3x%29%5Cimplies%20%5Ccfrac%7Bdy%7D%7Bdx%7D%3D%5Ccfrac%7B19-3x%7D%7Be%5E%7B3x%7D%7D)
set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there
there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema
Hello,
12x^4+39x^3+9x²=x²(12x²+39x+9)=x²(12x²+36x+3x+9)=x²(4x(3x+9)+(3x+9))
=x²(3x+9)(4x+1)
=3x²(x+3)(4x+1)
