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kienzie1
19.10.2021 •
Mathematics
caleb's grade was changed by -18 points because he did not complete some homework assignments. If he got -3 points for each assignment, how many assignments did he not complete?
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Ответ:
He got 6 assignments that he did not answer
Step-by-step explanation:
You have to divide 18 to 3
Wellcome
Ответ:
ANSWERS:
Question A. $1742.751361739
Question B. 23.1 years
WORKINGS:
Interest compounded continuously is calculated with the formula:
A = Pe^(rt)
Where,
P = Principal amount
r = Interest rate
t = Time in years
Question A. How much will Joe have in his account after 5 years
Given that Joe deposits $1,500 in the account
P = 1500
Given that the account pays 3% annual interest
r = 3/100
r = 0.03
Since we want to know how much Joe will have after 5 years
t = 5
A = Pe^(rt)
A = 1500e^(0.03 * 5)
A = 1500e^(0.15)
Using definition of logarithm:
0.15 = ln(A / 1500)
0.15 = ln(A) - ln(1500)
Add ln(1500) to both sides of the equation
0.15 + ln(1500) = ln(A) - ln(1500) + ln(1500)
0.15 + ln(1500) = ln(A)
ln(A) = 0.15 + ln(1500)
In (A) = 0.15 + 7.313220387
In (A) = 7.463220387
Solving for A
In (A) = 7.463220387
Therefore, A = e^(7.463220387) ; [e = 2.718281828]
A = 1742.751361739
Therefore, Joe have $1742.751361739 in his account after 5 years
Question B. How long will it take Joe to double his money?
A = Pe^(rt)
Given that Joe deposits $1,500 in the account
P = $1500
Given that the account pays 3% annual interest
r = 3/100
r = 0.03
Since we want to know how long it will take Joe to double his money
A = $1500 * 2 = $3000
Solving for t
A = Pe^(rt)
3000 = 1500e^(0.03t)
Using definition of logarithm
0.03t = In (3000/1500)
0.03t = ln(2)
Divide both sides of the equation by 0.03
0.03t/0.03 = ln(2)/0.03
t = ln(2) / 0.03
t = 0.693147181 / 0.03
t = 23.104906019
Therefore, it will take Joe 23.1 years to double his money.