When the town of Samuel Village first started its voluntary recycling program, 1200 of the town’s residence participated. The to

wn predicts that the number of people participating in the recycling program will increase by 35% each year. Which explicit rule can be used to determine the number of people participating in the program in the fifth year?

Mathematics

1 answer:

givi [52]3 years ago

5 0

$\bf \qquad \textit{Amount for Exponential Growth}
\\\\
A=P(1 + r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\to &1200\\
r=rate\to 35\%\to \frac{35}{100}\to &0.35\\
t=\textit{elapsed time}\\
\end{cases}
\\\\\\
A=1200(1+0.35)^t\implies A=1200(1.35)^t\implies \stackrel{\textit{fifth year}}{A=1200(1.035)^5}$

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Vadim26 [7]

Answer:

-4

-0.5, 12.25

x = -0.5

Step-by-step explanation:

The x intercepts are the values of x when y = 0 ie the roots of the equation
$-x^2 -x +12 = 0$

$x^2 + x - 12 = 0$

We can re-write the above as:
(x+4) (x-3) = 0
This gives the two roots as x = -4 and x = +3. Leftmost (smallest) root is -4 and rightmost(largest) root is +3

y intercept is when x = 0. Plugging into the original equation, y value at x = 0 is 12

Vertex x value is given by the formula -b/2a where a is the coefficient of x^2 and b the coefficient of x

Here a = -1, b= -1 so vertex x value = - (-1)/(-1).2 = - 1/2 = -0.5

Plugging this value of x into the original function gives the vertex y value
$y = - (0.5^{2}) - (-0.5) + 12\\= -0.25 + 0.5 + 12 = 12.25$

The line of symmetry is the vertical line corresponding to the vertex x value so line of symmetry is at x = -0.5

The graph of the quadratic function shows these values