How do I do the top problem?
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Answer:
The nth term of the geometric sequence 7, 14, 28, ... is:
Step-by-step explanation:
Given the geometric sequence
7, 14, 28, ...
We know that a geometric sequence has a constant ratio 'r' and is defined by
where a₁ is the first term and r is the common ratio
Computing the ratios of all the adjacent terms
The ratio of all the adjacent terms is the same and equal to
now substituting r = 2 and a₁ = 7 in the nth term
Therefore, the nth term of the geometric sequence 7, 14, 28, ... is:
Answer:
C(t)=5000 -10t
Step-by-step explanation:
There are many examples in the real world of relationships that are functions.
For example, imagine a tank full of water with a capacity of 5000 liters, this tank has a small hole, by which 10 liters of water are lost every hour.
If we call C the amount of water in the tank as a function of time, then we can write the following equation for C:
Where:
C (t): Amount of water in the tank as a function of time
: Initial amount of water in the tank at time t = 0
a: amount of water lost per hour
t: time in hours
Then the equation is:
The graph of C (t) is a line of negative slope. This relation is a function since for each value of t there is a single value of C.
Its domain is the set of all positive real numbers t between [0,500]
Because the time count starts at t = 0 when the tank is full and ends at t = 500 when empty
Its Range is the set of all positive real numbers C between [0,5000] Because the amount of water in the tank can never be less than zero or greater than 5000Litres