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3 years ago

Domain and range of the following graph

Mathematics

1 answer:

Readme [11.4K]3 years ago

8 0

Answer:

your anwers is option 3

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A culture started with 4000 bacteria after 8 hours it grew to 4400 bacteria. Predict how many bacteria will be present after 9 h

Leno4ka [110]

$\bf \qquad \textit{Amount for Exponential change}\\\\
A=P(1\pm r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{starting amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed period}\\
\end{cases}\\\\
-------------------------------\\\\$

$\bf A=P(1+r)^t\qquad 
\begin{cases}
\textit{hour 0, starting point}\\
t=0\qquad A=4000
\end{cases}\implies 182=ae^{k0}
\\\\\\
4000=P(1+r)^0\implies 4000=P
\\\\\\
thus\qquad A=4000(1+r)^t\\\\
-------------------------------\\\\$

$\bf A=P(1+r)^t\qquad 
\begin{cases}
\textit{8 hours later}\\
t=8\qquad A=4400
\end{cases}\implies 4400=4000(1+r)^8
\\\\\\
\cfrac{4400}{4000}=(1+r)^8\implies \cfrac{11}{10}=(1+r)^8\implies \sqrt[8]{\cfrac{11}{10}}=1+r
\\\\\\
\sqrt[8]{\cfrac{11}{10}}-1=r\implies 0.012\approx r\qquad thus\qquad \boxed{A=4000(1+0.012)^t}$

how many bacteria after 9 hours? well, 9hours later is just t = 9, plug that in, to get A

4 0

3 years ago

Read 2 more answers

The parking space shown at the right has an area of 209 ft2. A custom

jeyben [28]

Given:

The parking space shown at the right has an area of 209 ft².

A custom truck has rectangular dimensions of 13.5 ft by 8.5 ft.

To find:

Whether the truck fit in the parking space or not?

Solution:

If the area of the truck is more than the area of the parking space, then the truck cannot fit in the parking space otherwise it will fit in the parking space.

The area of a rectangle is:

$Area=length\times width$

Area of the rectangular truck is:

$Area=13.5\times 8.5$

$Area=114.75$

The area of the truck is 114.75 ft² which is less than the area of the parking space, 209 ft².

Therefore, the truck can fit in the parking space because the area of the truck is less than the area of the parking space.

3 0

3 years ago

What's the answer..............

ruslelena [56]

Aye the Answer is D ~hope that helps :)

7 0

4 years ago

Evaluate each finite series for the specified number of terms. 1+2+4+...;n=5

zaharov [31]

Answer:

Step-by-step explanation:

The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

1*2 = 2

2*2 = 4

The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

You may use either one of these formulas but I’ll use the first formula.

We are also given that n = 5, meaning we are adding up 5 terms in the series, substitute n = 5 in along with r = 2 and first term = 1.

$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

Therefore, the solution is 31.

__________________________________________________________

Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as: