Answer:
Step-by-step explanation:
Let the quadratic function be
We substitute into the equation to obtain;
We substitute to obtain;
We finally substitute to obtain;
We put equation (2) into equation (1) to get;
We add equation (4) and (5) to get;
We put into equation (5) to get;
The reqiured quadratic function is
Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P, where
∵ Angus has $3,000 he want to invest
∴ P = 3000
∵ The interest rate is compounded continuously
∵ Angus has $5,500 in 8 years
∴ A = 5500
∴ t = 8
→ Substitute them in the rule above to find r
∵ 5500 = 3000
→ Divide both sides by 3000
∴ =
→ Insert ㏑ in both sides
∵ ㏑( ) = ㏑(
)
→ Remember ㏑() = n
∴ ㏑( ) = 8r
→ Divide both sides by 8
∴ 0.07576697545 = r
→ Multiply it by 100% to change it to a percentage
∴ r = 0.07576697545 × 100%
∴ r = 7.576697545 %
→ Round it to the nearest hundredth
∴ r ≅ 7.58
∴ The interest rate is 7.58%