7 log(15/16)+6log(8/3)+5log(2/3)+log(32/25)by logarithm laws
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Answer:
<em>The age at which both companies charge the same premium is 44 years</em>
Step-by-step explanation:
<u>Graph Solution to System of Equations</u>
One approach to solving systems of equations of two variables is the graph method.
Both equations are plotted in the same grid and we find the intersection point(s) of both graphs. Those are the feasible solutions.
The annual premium p as a function of the client's age a for two companies are given as:
Company A: p= 2a+24
Company B: p= 2.25a+13
The graphs of both functions are shown in the image below.
The red line indicates the formula for Company A and the blue line indicates the formula for Company B.
It can be seen that both lines intersect in the point with approximate coordinates of (44,112).
The age at which both companies charge the same premium is 44 years
as you can see, the terms exponents, for the first term, starts at highest, 5 in this case, then every element it goes down by 1, till it gets to 0
for the second term, starts at 0, and every element it goes up by 1, till it gets to the highest
now, to get the coefficient, they way I get it, is "the product of the current coefficient and the exponent of the first term, divided by the exponent of the second term plus 1"
notice the first coefficient is always 1
so...how did we get 10 for the 3rd element? well, 5*4/2
how did we get 10 for the fourth element? well, 10*2/4
and from there, you can simplify the elements of the expansion by combining the coefficients
like for example, the 7th element of (3a+4b)⁸ will then be 1032192a²b⁶