Question 1125093: A 8-inch tall sunflower is planted in a garden and the height of the sunflower increases exponentially. 4 days after being planted the sunflower is 12.1446 inches tall.
a. What is the 4-day growth factor for the height of the sunflower?
b. What is the 1-day growth factor for the height of the sunflower?
c. What is the 6-day growth factor for the height of the sunflower?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the growth rate is exponential, therefore f = p * (1 + r) ^ n applies.
p is the present value = 8
f is the future value = 12.1446.
n is equal to 4 days.
you want to solve for r.
f = p * (1 + r) ^ n becomes 12.1446 = 8 * (1 + r) ^ 4
divide both sides of the formula by 8 to get 12.1446 / 8 = (1 + r) ^ 4
take the fourth root of both sides of the equation to get (12.1446 / 8) ^ (1/4) = 1 + r
subtract 1 from both sides of the equation to get (12.1446 / 8) ^ (1/4) = 1 = r
solve for r to get r = .110000839
1 + r is the 1 day exponential growth factor = 1.110000839.
the 4 day exponential growth factor is 1.110000839 ^ 4 = 1.518075.
the 6 day exponential growth factor is 1.110000839 ^ 6 = 1.870423035.
to find the growth factor, you assume the present value is 1.
for example:
1 * (1 + .110000839) ^ 4 = 1.518075.
the growth factor is then applied to the real present value.
in this case, the real present value was 8.
8 * (1 + .110000839) ^ 4 = 8 * 1.518075 = 12.1446.
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