Math Is Fun Forum

Mathegocart wrote:

Yes, the equation does represent continuous growth. As noted, you can convert that equation into the form of the continuous standard equation

with the substitution mentioned above.

I think it's not right, because I found the answer today
the form model without e and k like this :

is called non-continuous exponential models functions
because in case of increasing (a>1) while in case of model contain e, and k, if k is positive it's increasing continuously rate (because any positive number is acceptable and in case of base a there is numbers less then 1 are positive but not included)
and in case of decreasing (0<a<1) while in case of e, and k, here k is has to be negative <0 so it's continuously decreasing rate

so  now

its growth rate is not continuous,

am I right?

by the way I learned this today from a YouTube channel but I still don't understand why we can't called the base a a continuous if it's >1
I knew because it doesn't included the numbers that less than 1 and bigger than 0
but why? why this is a reasons that we can't call it continuously, what is meaning continuously in this case anyway? because every graph I draw in form of non-continuous exponential models I see them clearly in my naked eyes that they are continuous, I draw these random examples as in example I see them all goes beyond without end

https://i.ibb.co/bvG98qw/2021-12-16-060158.png

Mathegocart wrote:

No, because continuous growth is modeled with the equation

, where

is the ending value,

is the initial value,

is Euler's constant,

is the continuous growth rate, and

is the time that has passed.

What's stopping you from taking k = log(1.07)?

A roofing contractor purchases a shingle delivery truck with a shingle
elevator for $42,000. The vehicle requires an average expenditure of $9.50 per hour for fuel and maintenance, and the operator is paid $11.50 per hour.

(a) Write a linear equation giving the total cost C of operating this equipment for t hours. (Include the purchase cost of the equipment.)

I must add 9.50 + 11.50 to get 21

I then multiply 21 times t.

I finally add 21t to 42,000.

My equation is C(t) = 42,000 + 21t.

Is this correct?

(b) Assuming that customers are charged $45 per hour of machine use, write an equation for the revenue R
obtained from t hours of use.

I know the revenue formula is
Revenue = Quantity × Price.

I say the formula is R = 45t.

Is this right?

(c) Use the formula for profit P = R − C to write an equation for the profit obtained from t hours of use.

If R = 45t, and C = 42,000, I say the equation needed is P = 45t - 42,000.

Is this right?

(d) Use the result of part (c) to find the break-even point—that is, the number of hours this equipment
must be used to yield a profit of 0 dollars.

I am not too sure about part (d). What is break-even in the business world?

Thanks.

David wrote:

Sign up on imgur and once you upload an image, to embed look for the BBcode.
sample here:

[img]https://i.imgur.com/iW6bGpj.png[/img]

https://i.imgur.com/5bUJoIJ.png

Ok. I will play with this later on.

ganesh wrote:

See Circle Equations in MathIsFun/MathsIsFun.

Many more topics are covered in the MathIsFun/MathsIsFun website.

The 'Help me' topic is given to those who are in need.

An example can be provided; the members are expected to do the practice problems by themselves.

I may leave this site soon. I find that there isn't much participation here. I cannot even upload pictures needed for certain math problems. I made a few friends but that's about it, honestly. I am currently seeking a new math site.

It's too bad that yahoo answers has shut down. We all know that this is due to the current administration in Washington, DC. The main goal is to control the masses and to keep people from communicating with each other. This is happening everywhere across the internet.

Bob wrote:

If (a,b) is the centre of the circle and the radius is r then the equation will be

(x-a)^2 + (y-b)^2 = r^2.

This comes from Pythagoras' theorem.

For the first one you have both the centre and a point on the circumference so you can work out r.

For the second the centre will be half way along the diameter and the radius is half the length of the diameter,

Bob

For the second one, the midpoint formula comes into play, right?