GusGus11
15.03.2020 •
Mathematics
Business Calculus
Topic: Indefinite Integrals
The rate of disbursement of dQ/dt of a $9 million federal grant is proportional to the square of 100 - t, where t is the time (in days, 0 ≤ t ≤ 100) and Q is the amount that remains to be disbursed.
Find the amount that remains to be disbursed after 40 days.
*Assume the grant will be disbursed after 100 days.*
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Ответ:
$1.944 million
Step-by-step explanation:
dQ/dt = k(100-t)²
Q = -k(100-t)³/3 + c
t = 100, Q = 0
t = 0, Q = 9000000
0 = -k(100-100)³/3 + c
So c = 0
Q = -k(100-t)³/3
9000000 × 3 = -k(100)³
27000000 = -1000000k
k = -27
Q = 27(100-t)³/3
Q = 9(100-t)³
t = 40
Q = 9(60)³
Q = $1944000
Q = $1.944 million
Ответ:
a will work sorry if it is incorrect