Population are always modeled by exponential growth equation given by:
f(x)=a(1+b)^t
where:
a=original number
b=rate of growth
t=time
thus
f(x)=412(1.05)^t
the population after 9 months will be:
f(9)=412(1.05)^9=639.15=639
Answer:
119
Step-by-step explanation:
The nearest whole numbers from those listed are
10
3
106
The estimated sum = 119
The actual sum is 118.668
When you are doing a test, being able to estimate is a very powerful skill. 119 is close enough to the actual answer that you know your actual answer is likely correct.
Answer:
<em>Answer: C</em>
Step-by-step explanation:
<u>The Cosine Function</u>
The graph of a cosine function is a sinusoid that starts at its maximum value of 1 at x=0 and takes x=2π radians to complete a full cycle. The function of the parent cosine function is:
![y=\cos x](https://tex.z-dn.net/?f=y%3D%5Ccos%20x)
Both the amplitude A and the angular frequency w of a cosine can be modeled by the function
![y=A\cos(\omega x)](https://tex.z-dn.net/?f=y%3DA%5Ccos%28%5Comega%20x%29)
The graph of the cosine function shown in the figure has an amplitude of A=3 and it completes a full cycle at x=π/2, thus:
![\frac{\pi}{2}\omega =2\pi](https://tex.z-dn.net/?f=%5Cfrac%7B%5Cpi%7D%7B2%7D%5Comega%20%3D2%5Cpi)
Thus:
![\omega = 4](https://tex.z-dn.net/?f=%5Comega%20%3D%204)
Therefore, the equation of the sinusoid is:
![y=3\cos (4x)](https://tex.z-dn.net/?f=y%3D3%5Ccos%20%284x%29)
Answer: C
Answer: A
Step-by-step explanation:
3x² - 10x + 5 = 0
a = 3 b = -10 c = 5
Δ = b²- 4ac = 100 - 4.3.5 = 40 > 0 => have 2 solutions
=> x =
or x = ![\frac{10-\sqrt{40} }{6}](https://tex.z-dn.net/?f=%5Cfrac%7B10-%5Csqrt%7B40%7D%20%7D%7B6%7D)