# Composite functions rates of change

#### littlord123

##### New member
The area of a circle is 𝐴(𝑟)=𝜋𝑟2. The radius of a circular oil spill is increasing at a speed of 1/2 m per second.

a) Express the radius as a function of time

b) Find the composite function A(t)

c) When is the area 100pi m^2?

I'm having a tough time with this unit, I missed quite a bit of the lesson because my internet cut out.

#### Subhotosh Khan

##### Super Moderator
Staff member
The area of a circle is 𝐴(𝑟)=𝜋𝑟2. The radius of a circular oil spill is increasing at a speed of 1/2 m per second.

a) Express the radius as a function of time

b) Find the composite function A(t)

c) When is the area 100pi m^2?

I'm having a tough time with this unit, I missed quite a bit of the lesson because my internet cut out.
Please post the COMPLETE problem. As posted - it cannot be solved

Can you express the following as a mathematical equation?

The radius of a circular oil spill is increasing at a speed of 1/2 m per second.​

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

#### littlord123

##### New member
This is the question I was presented and I do not understand how to answer it.

#### Subhotosh Khan

##### Super Moderator
Staff member
This is the question I was presented and I do not understand how to answer it.
If that is the EXACT question as presented to you, then it cannot be answered.

Can you post a photograph of the assignment?

#### skeeter

##### Elite Member
The area of a circle is 𝐴(𝑟)=𝜋𝑟2. The radius of a circular oil spill is increasing at a speed of 1/2 m per second.

a) Express the radius as a function of time

b) Find the composite function A(t)

c) When is the area 100pi m^2?

I'm having a tough time with this unit, I missed quite a bit of the lesson because my internet cut out.
a) $$\displaystyle r = \frac{t}{2}$$

continue with the rest of the problem ...

#### Dr.Peterson

##### Elite Member
The area of a circle is 𝐴(𝑟)=𝜋𝑟2. The radius of a circular oil spill is increasing at a speed of 1/2 m per second.

a) Express the radius as a function of time

b) Find the composite function A(t)

c) When is the area 100pi m^2?

I'm having a tough time with this unit, I missed quite a bit of the lesson because my internet cut out.
I think we can assume it's intended to mean, "The radius of a circular oil spill is increasing at a constant speed of 1/2 m per second, starting at 0 when t=0".

What we can't assume is that we know where you are having trouble. Does your textbook have no similar examples?

The composite function A(t) means A(r(t)); you've been told what to write for (a), which is r(t), so continue. Then in part (c) you'll be solving for t. If you show any work, or ask specific questions, we can do better at helping with the point you need help on.

#### Harry_the_cat

##### Senior Member
The area of a circle is 𝐴(𝑟)=𝜋𝑟2. The radius of a circular oil spill is increasing at a speed of 1/2 m per second.

a) Express the radius as a function of time

b) Find the composite function A(t)

c) When is the area 100pi m^2?

I'm having a tough time with this unit, I missed quite a bit of the lesson because my internet cut out.
(a)"The radius of a circular oil spill is increasing at a speed of 1/2 m per second." This can be interpreted as
$$\displaystyle \frac{dr}{dt}=\frac{1}{2}$$ where $$\displaystyle t$$ is the time in seconds.

This then gives
$$\displaystyle r = \frac{1}{2}t +c$$

Assuming that $$\displaystyle r=0$$ when $$\displaystyle t=0$$, then $$\displaystyle c=0$$.

So $$\displaystyle r = \frac{1}{2}t$$

(b) You are given $$\displaystyle A(r)$$. Use (a) to find $$\displaystyle A(t)$$.

(c) Find $$\displaystyle t$$ when $$\displaystyle A=100\pi$$.

Show us what you can do for (b) and (c).