Answer:
8 percent loss
Step-by-step explanation:
The given formula is f(x) = 20(1.2)^x
The formula is the starting amount multiplied by 1 + the percentage raised to the number of weeks.
A) the percent increase is 20% ( 1.2 in the formula is 1 +20% as a decimal)
B) the original amount is $20
C) for 2 weeks, replace x with 2 and solve:
20(1.2)^2
20(1.44) = $28.80
After 2 weeks the coupon is $28.80
D) To solve for the number of weeks (x) set the equation equal to $100:
100 = 20(1.2)^x
Divide both sides by 20:
5 = 1.2^x
Take the natural logarithm of both sides:
ln(5) = ln(1.2^x)
Use the logarithm rule to remove the exponent:
ln(5) = x ln(1.2)
Divide both sides by ln(1.2)
x = ln(5) / ln(1.2)
Divide:
X = 8.83
At 8.83 weeks the coupon would be $100, so after 9 weeks the coupon would be greater than $100
The answer is 9 weeks.
Write the vertex form of the equation and find the necessary coefficient to make it work.
.. y = a*(x +3)^2 -2
.. = ax^2 +6ax +9a -2
You require the y-intercept to be 7. So, for x=0, you have
.. 9a -2 = 7
.. 9a = 9
.. a = 1
The equation you seek is
.. y = x^2 +6x +7
U=units
A=πr²
=π(44)²
=6082.12u²
6082.12/121= 50.27
A=πr²
50.27=πr²
r²=50.27/π
r=√16
r=4u