Math Help - Average Rate of Change - Populuation

1. Average Rate of Change - Populuation

The population of a town is modelled by P(t) = 6t^2 + 110t + 3000, where P is the population and t is the number of years since 1990.

a) find the average rate of change in population between 1995 - 2005

b) Estimate the rate at which the population is chaning in 2005.

* I am currently taking Calculus and Vectors for the first time through corrospondance, with no textbook or other material support. I would really appreciate any help.
Thank you very much in advance.

2. Do you know how to differentiate an expression?

The rate of change of population is the gradient of the graph of y = 6t^2 + 110t + 3000.

To find the gradient at any point, we make use of differentiation.

In this case, the differentiation is done by 'lowering' the power of the variable. Let me give you an example:

y = 2x

Reduce the power of x by 1, this means that x will go from x^1 to x^0 = 1, hence, differentiating [tex]y = 2x[tex] gives $y' = 2 \times 1 = 2$

$y = 2x^2$

Differentiate to give:

$y' = 4x$

Basically, if you have $y = ax^n$, the derivative is $y' = anx^{n-1}$

Now, can you try your problem?

3. This problem specifically asks for the average rate of change so the derivative is inappropriate.

1) Find the population in 1995 and in 2005. Since "t is the number of years since 1990." just evaluate the population expression, P(t), for t= 5 and t= 15.

2) Find the change in population between 1995 and 2005. Subtract the values you got in (1).

3) Find the average rate of change. Divide by the number of years: 2005- 1995= 10 years.