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There are 250 wolves in a national park. the wolf population is increasing at a rate of 16% per year. write an exponential model

Helga [31]

$\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ A=250(1 + 0.16)^{t}\implies A=250(1.16)^t \\\\[-0.35em] ~\dotfill$

$A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill &1000\\ P=\textit{initial amount}\dotfill &250\\ r=rate\to 16\%\to \frac{16}{100}\dotfill &0.16\\ t=\textit{elapsed time} \end{cases} \\\\\\ 1000=250(1.16)^t\implies \cfrac{1000}{250}=1.16^t\implies 4=1.16^t \\\\\\ \log(4)=\log(1.16^t)\implies \log(4)=t\log(1.16) \\\\\\ \cfrac{\log(4)}{\log(1.16)}=t\implies \stackrel{\textit{about 9 years and 4 months}}{9.34\approx t}$

7 0

1 year ago

GEOMETRY PROOFS!

yarga [219]

From the given figure ,

RECA is a quadrilateral

RC divides it into two parts

From the triangles , ∆REC and ∆RAC

RE = RA (Given)

angle CRE = angle CRA (Given)

RC = RC (Common side)

Therefore, ∆REC is Congruent to ∆RAC

∆REC =~ ∆RAC by SAS Property

⇛CE = CA (Congruent parts in a congruent triangles)

Hence , Proved

Additional comment:-

SAS property:-

"The two sides and included angle of one triangle are equal to the two sides and included angle then the two triangles are Congruent and this property is called SAS Property (Side -Angle-Side)

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Consider the proof. Given: Segment AB is parallel to line DE. Prove: AD/DC = BE/EC What is the missing statement in Step 5? A.) AC = BC B.) AC/DC = BC/EC C.) AD...

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4 0

1 year ago

Read 2 more answers

Could somebody help please

xz_007 [3.2K]

If you have zero dollars you can’t buy anything

7 0

2 years ago

When Raphael solved the system below by using the method of elimination, he changed the second equation to -8x-2y=-2 what proper

galben [10]

For this case, what we are going to do is use the following property:
Multiply an equation by a scalar.
In this case, the scalar will be:
k = -2
We have then that equation 2 will be:
k * (4x + y) = k * 1
-2 * (4x + y) = - 2 * 1
-8x-2y = -2
Answer:
The property that justifies this manipulation is:
Multiply an equation by a scalar.

4 0

2 years ago

The Department of Homeland Security wants to test a computer virus that it has developed to combat hackers. They plan to test ru

ra1l [238]

Answer:

Simple random sampling

Observational study

Step-by-step explanation:

Since in the given situation it is mentioned that department wants to test the computer virus and have to run the virus on the random selected computers so here the simple random sampling would be done and based on the simple random sampling the observational study would be done

Therefore the above represent the answer

8 0

2 years ago