Answer:
1) Let's suppose that you go in a straight line, in a car that moves at a constant speed of 80km/h.
Then the distance from your house (assuming that you start the drive in your house) can be modeled with a linear equation:
D(t) = 80km/h*t
where t is time in hours.
This will be a linear function.
2) Suppose that you have a population of some animal, that grows by 2% each month, and initially, there are 100 individuals of that animal.
Then the first month, the population is 100.
The second month the population increased by a 2%, then it will be:
100 + 100*0.02 = 100*(1.02)
The third month, the population will be 100*(1.02) + 0.2*100*(1.02) = 100*(1.02)^2.
and so on, this is an exponential relation, where the population as a function of the number of months, can be written as:
P(m) = 100*(1.02)^(m - 1)
3) Suppose that you have $100 saved, and each month you can save another $80, let's find a function that says the amount of money that you have saved as a function of the number of months. S(m)
The month number zero (before you started saving) you had $100 saved.
S(0) = $100.
One month after, you have saved $80 more, then you have:
S(1) = $100 + $80
Another month after, you have:
S(2) = $100 + $80 + $80 = $100 + 2*$80
And so on, you already can see the pattern, after m months, you will have:
S(m) = $100 + m*$80 saved.
If a1=1.6 then:
The solution for all these equations is: q=0.5. We have: a1=1.6, q=0.5 and this is geometric sequence.
