Kindred invested $38,976 into his first company. His investment decreased by 3.5% each year over the first 3 years. Which expone
ntial decay model could Kindred use to determine the amount his investment will be worth if it continues to decrease at the same rate?
1 answer:
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When two lines intersect, the angles across from the intersection (the "X") are congruent (equal), and referred to as "vertical angles."
So by the rule of vertical angles are congruent, we can set them equal:
to factor we need the factors of 84:
1×84, 2×42, 3×28, 4×21, 6×14
Now we need one of those factors ×2 ( from the x^2 term) minus the other factor to equal 13 (the middle term)
it turns out that if we use 4×21: 4×2 = 8
and 21-8 = 13. Woohoo! we got it
So now we have:
Now set each factor = 0
1) 2x - 21 = 0 and 2) x + 4 = 0
1) 2x - 21 = 0, 2x = 21, x = 21/2 = 10.5
2) x + 4 = 0, x = -4
Now we plug in each answer to check:
1) x = 10.5
1/2x + 42 = 1/2(10.5) + 42 = 5.25 + 42 = 47.25
47.25 = 47.25
BAM SO IT LOOKS LIKE THAT'S IT!!
But let's check 2) first:
2) x = -4
1/2x + 42 = 1/2(-4) + 42 = -2 + 42 = 40
40 = 40, so both work!!
But it asks for m<1, and <1 is supplementary because it lies on same line, meaning the sum of both = 189
Therefore m<1 = 180 - 47.25 = 132.75°
OR m<1 = 180 - 40 = 140°
So by the rule of vertical angles are congruent, we can set them equal:
to factor we need the factors of 84:
1×84, 2×42, 3×28, 4×21, 6×14
Now we need one of those factors ×2 ( from the x^2 term) minus the other factor to equal 13 (the middle term)
it turns out that if we use 4×21: 4×2 = 8
and 21-8 = 13. Woohoo! we got it
So now we have:
Now set each factor = 0
1) 2x - 21 = 0 and 2) x + 4 = 0
1) 2x - 21 = 0, 2x = 21, x = 21/2 = 10.5
2) x + 4 = 0, x = -4
Now we plug in each answer to check:
1) x = 10.5
1/2x + 42 = 1/2(10.5) + 42 = 5.25 + 42 = 47.25
47.25 = 47.25
BAM SO IT LOOKS LIKE THAT'S IT!!
But let's check 2) first:
2) x = -4
1/2x + 42 = 1/2(-4) + 42 = -2 + 42 = 40
40 = 40, so both work!!
But it asks for m<1, and <1 is supplementary because it lies on same line, meaning the sum of both = 189
Therefore m<1 = 180 - 47.25 = 132.75°
OR m<1 = 180 - 40 = 140°