If (m,2m+1) is a solution of the equation 4x +2y=8 then the value of m
1 answer:
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Answer:
(a) The value of C is 1.
(b) In 2010, the population would be 1.07555 billions.
(c) In 2047, the population would be 1.4 billions.
Step-by-step explanation:
(a) Here, the given function that shows the population(in billions) of the country in year x,
So, the population in 2000,
According to the question,
(b) Similarly,
The population in 2025,
(∵ C = 1)
Again according to the question,
Taking ln both sides,
Thus, the function that shows the population in year x,
...... (1)
The population in 2010,
Hence, the population in 2010 would be 1.07555 billions.
(c) If population P(x) = 1.4 billion,
Then, from equation (1),
Therefore, the country's population might reach 1.4 billion in 2047.
Answer:
A horizontal translation of 5 units to the left.
Step-by-step explanation:
Given the parent linear function:
To shift vertically n units, we can simply add n to our function. Hence:
So, a vertical shift of 5 units up implies that n=5. So:
As given.
However, to shift a linear function horizontally, we substitute our x for (x-n), where n is the horizontal shift. So:
Where n is the horizontal shift.
For example, if we shift our parent linear function 1 unit to the right, this means that n=1. Therefore, our new function will be:
Or:
We notice that this is also a vertical shift of 1 unit downwards.
Therefore, we want a number n such that -n=5.
So, n=-5.
Therefore, it we shift our function 5 units to the left, then n=-5.
Then, our function will be:
Hence, we can achieve f(x)=x+5 from f(x)=x using a horizontal translation by translating our function 5 units to the left.