I need help with questions.

I am currently studying year 12 Maths methods and am trying to complete questions set by my teacher. I missed a few weeks of school due to illness and need to catch up (hence the questions). My teacher doesn't have time after school, and isn't will to help me during lunch time and recess, I have some questions that I need help with and if I don't complete these I will not be prepared for my upcoming SAC. I have posted the questions I need help with below. If someone could please give me full worked examples and maybe some pointers on solving them, that would be amazing. I know it's alot to ask, but this is a last resort. I want to understand these questions and how to solve them, so if someone could please explain what they are doing while they do worked examples, that would be awesome. I have a Casio Classpad calculator that can assist me.

*Note:

A bold **x** means the letter. A non bold x, means multiply.

The first one is:

Sketch the graph F:R ->R, F(**x**)=2Log_{e} (**x**-13)

Number 2:

(this was quite a long question, so I have summirised and taken the key points, It was a worded question)

A factory moved into town. After it's arivle the local population grows from 10,000 to 12,000 in 2 years. Using P=Ae^{kt} were P= population and t=years to find the population after 4 years.

Number 3:

Solve for **x**

A) 8^{2(2x-1)}

------- = 32^{(x+2)} (This is ment to be 8^{2(2x-1)} over 2**x** =32^{(x+2)})

2**x**

B) 4(2^{2x}=5-2^{x})

Number 4:

|**x**-4|+|**x**+2|+|2**x**+1| Sketch that, and state the domain and range.

Number 5:

Given that log_{a}b=1.5 and log_{a}c= 0.5 find the value of:

A) log_{a}(bc)

B) log_{a} Square root c

C) log_{a}b^{2}

Any help would be awesome, and much appreciated :) I have been alright catching up on all my other subjects, but this one is two hard without the help of my teacher.

Re: I need help with questions.

**Number 2 :**

Let :

$\displaystyle P_1=Ae^{kt_1}$

$\displaystyle P_2=Ae^{kt_2}$

$\displaystyle P_3=Ae^{kt_3}$

hence :

$\displaystyle \frac{P_2}{P_1} = e^{k(t_2-t_1)} \Rightarrow k=\frac{\ln\left(\frac{P_2}{P_1}\right)}{t_2-t_1}$

therefore :

$\displaystyle \frac{P_3}{P_2} = e^{k(t_3-t_2)} \Rightarrow P_3=P_2 \cdot e^{k(t_3-t_2)}$

**Number 3 :**

$\displaystyle A)~8^{2(2x-1)}=2x \cdot 32^{(x+2)} \Rightarrow 2^{6(2x-1)}=2x \cdot 2^{5(x+2)} \Rightarrow 1=2x \cdot 2^{(-7x+16)}\Rightarrow$

$\displaystyle \Rightarrow 1=2^{17} \cdot x \cdot 2^{-7x} \Rightarrow \frac{-7}{2^{17}}=-7x \cdot 2^{-7x} \Rightarrow \frac{-7}{2^{17}}=-7x \cdot e^{-7x \cdot \ln 2} \Rightarrow$

$\displaystyle \Rightarrow \frac{-7 \cdot \ln 2}{2^{17}}=-7x \cdot \ln 2 \cdot e^{-7x \cdot \ln 2} \Rightarrow -7x \cdot \ln 2 = W\left(\frac{-7 \cdot \ln 2}{2^{17}}\right) \Rightarrow $

$\displaystyle \Rightarrow x= \frac{-W\left(\frac{-7 \cdot \ln 2}{2^{17}}\right)}{7\cdot \ln 2}$

where W is Lambert W function .

**Number 5 :**

$\displaystyle A) ~\log_{a}(bc)=\log_{a}b+\log_{a} c$

$\displaystyle B)~ \log_{a} \sqrt c=\frac{1}{2} \cdot \log_{a} c$

$\displaystyle C) ~ \log_{a} b^2=2 \cdot \log_{a} b$

Re: I need help with questions.

Quote:

Originally Posted by

**Jamie772** I am currently studying year 12 Maths methods and am trying to complete questions set by my teacher. I missed a few weeks of school due to illness and need to catch up (hence the questions). My teacher doesn't have time after school, and isn't will to help me during lunch time and recess, I have some questions that I need help with and if I don't complete these I will not be prepared for my upcoming SAC. I have posted the questions I need help with below. If someone could please give me full worked examples and maybe some pointers on solving them, that would be amazing. I know it's alot to ask, but this is a last resort. I want to understand these questions and how to solve them, so if someone could please explain what they are doing while they do worked examples, that would be awesome. I have a Casio Classpad calculator that can assist me.

*Note:

A bold **x** means the letter. A non bold x, means multiply.

The first one is:

Sketch the graph F:R ->R, F(**x**)=2Log_{e} (**x**-13)

Number 2:

(this was quite a long question, so I have summirised and taken the key points, It was a worded question)

A factory moved into town. After it's arivle the local population grows from 10,000 to 12,000 in 2 years. Using P=Ae^{kt} were P= population and t=years to find the population after 4 years.

Number 3:

Solve for **x**

A) 8^{2(2x-1)}

------- = 32^{(x+2)} (This is ment to be 8^{2(2x-1)} over 2**x** =32^{(x+2)})

2**x**

B) 4(2^{2x}=5-2^{x})

Number 4:

|**x**-4|+|**x**+2|+|2**x**+1| Sketch that, and state the domain and range.

Number 5:

Given that log_{a}b=1.5 and log_{a}c= 0.5 find the value of:

A) log_{a}(bc)

B) log_{a} Square root c

C) log_{a}b^{2}

Any help would be awesome, and much appreciated :) I have been alright catching up on all my other subjects, but this one is two hard without the help of my teacher.

Do you live in Melbourne? If so, I'm a private maths tutor. Send me a PM if you want to arrange some tutoring to catch up.