Step-by-step explanation:
dA/dt = 6 − 0.02A
dA/dt = -0.02 (A − 300)
Separate the variables.
dA / (A − 300) = -0.02 dt
Integrate.
ln(A − 300) = -0.02t + C
Solve for A.
A − 300 = Ce^(-0.02t)
A = 300 + Ce^(-0.02t)
Use initial condition to find C.
50 = 300 + Ce^(-0.02 × 10)
50 = 300 + Ce^(-0.2)
-250 = Ce^(-0.2)
C = -250e^(0.2)
A = 300 − 250e^(0.2) e^(-0.02t)
A = 300 − 250e^(0.2 − 0.02t)
Answer:
Interest earned = 2713.8
Explanation:
We will solve this problem on two steps:
1- get the final amount after three years
2- get the interest earned by subtracting the initial amount from the final one.
1- getting the final amount after 3 years:
The formula that we will use is as follows:
A = P (1 + r/n)^(nt)
where:
A is the final amount we want to calculate
P is the initial amount = 6300
r is the interest = 0.12
n is the number of compounds per year =12
t is time in years = 3
Substitute to get the final amount:
A = P (1 + r/n)^(nt)
A = 6300 (1 + 0.12/12) ^ (12*3)
A = 9013.8
2- getting the interest earned:
Interest earned = final amount - initial amount
Interest earned = 9013.8 - 6300
Interest earned = 2713.8
Hope this helps :)
