19. the population of jose's town in 1995 was 2400 and the population in 2000 was
4000, let x represent the number of years since 1995. write a linear equation, in slope-
intercept form, that represents this data.

The linear equation in slope intercept form for population of Jose's town is y = 320x + 2400.

Solution:

Given, the population of Jose's town in 1995 was 2400 and the population in 2000 was 4000,  

Let x represent the number of years since 1995.  

We have to write a linear equation, in slope- intercept form, that represents this data.

Now, let the change in population per year be p.

Then, population in a year = population change per year number of years + population in 1995.

⇒population in a year = p x + population in 1995

⇒ population in a year = p x + 2400

Here we have an case that, population in 2000 is 4000  

Then, number of years since 1995 = 5  

So, 4000 = p 5 + 2400 ⇒ 5p = 4000 – 2400 ⇒ 5p = 1600 ⇒ p = 320

Then, our equation will be population in a year = 320x + 2400  

Considering the population in a year as y ⇒ y = 320x + 2400.

Hence, the linear equation in slope intercept form is y = 320x + 2400.

can you rephrase the question ? it is unclear : -)

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for