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.*

$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

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

x + 4/7

step-by-step explanation:

use cymath