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.
Answer: (-2, 2) and (4, 8)
There are two solutions because the two functions cross each other twice.
Answer:
Step-by-step explanation:
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Up
Vertex:
(
1
,
−
2
)
Focus:
(
1
,
−
23
12
)
Axis of Symmetry:
x
=
1
Directrix:
y
=
−
25
12
x
y
−
1
10
0
1
1
−
2
2
1
3
10
2.3
4.14
6.2
8.-9
10.-1
12.-13
14.-20
16.10
18.-2
20.-6
22.16
Answer: 27.42 units
Step-by-step explanation:
6 + 6 + 6 = 18
C= 1/2 3.14d
1/2 x 3.14 x 6
3.14 x 3
=9.42
18+9.42 = 27.41
