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Answer:
The interest rate is 7.58%
Step-by-step explanation:
Compound continuous interest can be calculated using the formula:
A = P, where
- A is the future value of the investment, including interest
- P is the principal investment amount (the initial amount)
- r is the interest rate in decimal
- t is the time the money is invested for
∵ 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%
400 children and 600 adults bought tickets.
Step-by-step explanation:
Given,
Cost of one child ticket = $14
Cost of one adult ticket = $32
Total attendance = 1000
Revenue generated = $24800
Let,
x be the number of children.
y be the number of adults.
According to given statement;
x+y=1000 Eqn 1
14x+32y=24800 Eqn 2
Multiplying Eqn 1 by 14
Subtracting Eqn 3 from Eqn 2
Dividing both sides by 18
Putting y=800 in Eqn 1
400 children and 600 adults bought tickets.
Keywords: linear equations, subtraction
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