Composite Functions and Exponential Growth

In summary, the speaker is asking for help with some questions on a problem set they are working on. They mention that the first question starts off easy but becomes more challenging later on, and provide a formula for the rate of spread. They also mention using chain rule and product rule for 1b, and solving for x in the second question to find the coordinates (-$\pi$/2, 0). They thank the listener in advance.
  • #1
ardentmed
158
0
Hey guys,

Few more questions for the problem set I've been working on. I'm doubting some of my answers and I'd appreciate some help.

Question:
08b1167bae0c33982682_12.jpg


The first one starts off easy but I found that it gets progress more challenging later on. So the rate of spread should be p'(t) which is:

p'(t) = 5/[e^.5t * (1+10e^(-.5t))^2]


As for 1b, I just used chain rule and product rule together to get:

f''(x) = 6xy'(x^2) + 4(x^3)g''(x^2)And finally, for the second question, if the tangent it horizontal, then dy/dx = 0, right?

Therefore, you solve for x, which leads you to:

sinx=-1
x=arcsin(-1)
x= -$\pi$/2


Which leads to ( -$\pi$/2 , 0 ) as the co-ordinates after substituting x = -$\pi$/2 into the original function.

Thanks in advance.
 
Physics news on Phys.org
  • #2
I suspect you have posted the wrong image (containing the questions) here...
 

FAQ: Composite Functions and Exponential Growth

What is a composite function?

A composite function is a function that is composed of two or more functions. It involves taking the output of one function and using it as the input for another function.

How do you find the composite of two functions?

To find the composite of two functions, you plug in the output of one function into the input of the other function. For example, if f(x) and g(x) are two functions, the composite function would be written as f(g(x)).

What is exponential growth?

Exponential growth is a type of growth that occurs when the rate of increase of a quantity is proportional to its current value. This means that the larger the quantity, the faster it will grow.

How do you calculate the growth rate in exponential growth?

The growth rate in exponential growth is calculated by taking the difference between the final value and the initial value, dividing it by the initial value, and then multiplying by 100 to get a percentage. This can also be expressed as a formula: growth rate = ((final value - initial value) / initial value) x 100%.

What real-life situations can be modeled using composite functions and exponential growth?

Composite functions and exponential growth can be used to model a variety of real-life situations, such as population growth, compound interest, and the spread of diseases. They can also be used in fields like finance, economics, and biology to make predictions and analyze data.

Similar threads

Back
Top