Solution A small town decides to conduct a fund-raising drive for a new park facilities for kids. The cost is $50 000. The initial amount given by City Hall is $8 000. The contribution to the fund F is increasing at a rate proportional to the difference between the cost of $50 000 and the amount F at time t in months. After one month, $36 000 is in the fund. How much will be in the fund after 3 months

The fund, F, after 3 months = $48,442.25

Step-by-step explanation:

Amount to be made = $50000

Initial amount = F₀ = $8000

The contribution to the fund F is increasing at a rate proportional to the difference between the cost of $50,000 and the amount F at time t in months.

Noting that F ≤ 50,000

(dF/dt) ∝ (50,000 - F)

k = constant of proportionality

F' = k(50000 - F)

dF/(50000 - F) = k dt

∫ dF/(50000 - F) = ∫ kdt

- In [50,000 - F] = kt + c

c = constant of integration

At t = 0, F = $8000

- In [50,000 - 8,000] = 0 + c

c = - In 42,000 = - 10.645

- In [50,000 - F] = kt - 10.645

After one month, $36,000 is in the fund.

at t = 1 month, F = $36,000

- In [50,000 - 36,000] = k - 10.645

k - 10.645 = - In 14,000 = - 9.547

k = 10.645 - 9.547 = 1.098

- In [50,000 - F] = 1.098t - 10.645

In [50,000 - F] = 10.645 - 1.098t

At t = 3 months,

In [50,000 - F] = 10.645 - 1.098(3) = 7.351

50,000 - F = e⁷•³⁵¹ = 1557.7535

F = 50,000 - 1557.7535 = $48,442.2465

The fund, F, after 3 months = $48,442.25

Hope this Helps!!!

answer

a,b, and d

explanation

a reflection angle is more than

but less than;

an angle that measures

is a reflex angle.(true)

an angle that measures less than

is acute.(true)

provided we are considering angles greater or equal to zero.

an acute angle lies in the range.

an obtuse angle is less than 180° but more than 90°

an angle that measures 300° is obtuse (false)

an angle that measures 65° is an acute angle.(true)