On the day that a certain celebrity proposes marriage,

10 people know about it. Each day afterward, the number of people who know triples.

Write a function that gives the total number n(t) of people who know about the celebrity proposing t days after the celebrity proposes.

The answer is n(t) = 10 x 3^{t - 1}

Step-by-step explanation: If on the first day of proposing 10 persons knew about it, then the first number of course shall be 10. Then the number of people that are aware of the proposal becomes triple (that is, times 3), it means that on day 2 they would be 10 times 3, and so on for all subsequent days.

What we have is a geometric progression where the next number in the sequence is derived as the previous number times a common ratio (which is r). Since the number triples daily, the common ratio here is 3. We have therefore,

A = 10

R = 3

The formula for a geometric sequence like this one is given as;

A(n) = A x R^{n - 1}

Where A(n) is the term we need to calculate (nth term) and n is the number of the term in the sequence.

To find out how many people know about the proposal t days after the celebrity proposes, we insert the known values as follows;

n(t) = A x R^{n - 1}

n(t) = 10 x 3^{t - 1}

(Where t is the number of days after the proposal)

if the eqn of the parabola is f(x) = (x-4)(x+2), we need to mult. this out to find the coordinates of the vertex.

then f(x) = x^2 + 2x - 4x - 8, and f(x) = x^2 - 2x - 8.

one way in which you can find the vertex is to calculate x = -b / (2a).   here, that comes to

        )

x = = 1.   f(1) = 1^2 - 2(1) - 8 = - 9.   vertex is at (1, -9).

        2(1) 

find another point on the curve:   let x=0, for which y=-8.   then (0, -8) is on the curve.   plot the vertex and this point and draw a smooth parabola thru both.

hope this

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step-by-step explanation: