Answer:
A. -4 and 4
B. No solution.
Step-by-step explanation:
The given equation is
A.
Equate the denominators equal to 0 to find the restrictions on the variable.
Therefore, .
B.
We have,
Multiply both sides by (x-4)(x+4).
Add 4 on both sides.
Divide both sides by 5.
Here the solution is x=4 but it is the restricted value.
Therefore, the given equation has no solution.
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Explanation:
We have these two functions
which represent the amounts for his friend and William in that order. Strangely your teacher mentions William first, but then swaps the order when listing the exponential function as the first. This might be slightly confusing.
The table of values is shown below. We have t represent the number of years and t starts at 0.5. It increments by 0.1
The f(t) and g(t) columns represent the outputs for those mentioned values of t. For example, if t = 0.5 years (aka 6 months) then f(t) = 12.48 and that indicates his friend has 12,480 dollars in the account.
I've added a fourth column labeled |f - g| which represents the absolute value of the difference of the f and g columns. If f = g, then f-g = 0. The goal is to see if we get 0 in this column or try to get as close as possible. This occurs when we get 0.09 when t = 1.0
So we don't exactly get f(t) and g(t) perfectly equal, but they get very close when t = 1.0
It turns out that the more accurate solution is roughly t = 0.9925 which is close enough. I used a graphing calculator to find this approximate solution.
It takes about a year for the two accounts to have the same approximate amount of money.
