POPULATION DECAY 1

A settlement has a population of 2000 people. Each year 12%of the people leave the settlement. How many people will remain after 3 years?

solution

f(t) = A ( 1 -12/100)^t

= 2000(1 – 0.12)^t

= 2000 x (0.88)³

= 2000 x 0.88x 0.88x 0.88

= 2000 x 0.681472

= 1362.944 (1363 approximate)

Therefore there will be 1363 people remaining after three years of decay

TRY THIS………….

A settlement has a population of 5000 people. Each year 5%of the people leave the settlement. How many people will remain after 4 years?

SETS 1

If n(A)= 36 , n(B)= 50 and n(AuB)=65, find n(AnB).

Solution

n(AuB) = n(A) + n(B) - n(AnB)

       65 = 36 + 50 - n(AnB)

       65 = 86  - n(AnB)

       65 - 86 = - n(AnB)

              -21 = - n(AnB)

21 = n(AnB) (after dividing by -1 on both sides)

Hence n(AnB) = 21 answer

TRY THIS……………………

If n(A)= 35 , n(B)= 45 and n(AuB)=70, find n(AnB).

MAKING THE SUBJECT 1

If M = u(b + s)    make s the subject of the formula.

             (b – s)

Solution

M = u(b + s)   

          (b – s)

(b – s) x M = u(b + s) x (b – s) 1 multiply by(b-S) on both sides.

                         (b – s) 1

(b – s) x M = u(b + s) open the brackets on both sides.

Mb – Ms = ub + us

Mb – ub = Ms + us   (collect the terms containing s together)

Mb – ub = s(M + u)

Mb – ub = s(M + u) ¹               Divide by (M + u) on both sides.

(M + u)         (M + u) ₁

Mb – ub = s

(M + u)        

Hence  s =   Mb – ub

                      (M + u)   

   TRY THIS………………….

 If M = u(a + e)    make e the subject of the formula.

               (a – e)

%'GE PROFIT 1

A man got a profit of 200/= after selling an item for 7000/=. Find the percentage profit.

Solution

%’ge profit = Profit   X  100    where B. P. represents Buying Price.

                         B.P

%’ge profit = 200   X  100   

                        7000

%’ge profit = 2⁶/7%   

                       

Hence Percentage Profit is 2⁶/7%   

TRY THIS………………….

A man got a profit of 400/= after selling an item for 8000/=. Find the percentage profit.

RADIAN TO DEGREES 1

Change ^5∏/4 radians into degrees.

Solution

Ө = 180⁰ x s                but s = ^5∏/4

       ∏

Ө = 180⁰  x  5∏              

       ∏     4

Ө =  ⁴⁵180  x  5∏ ¹             

          ₁∏     4₁

= 45 x 5

= 135

Hence ^5∏/4 radian is equal to 135⁰.

TRY THIS………………….

Change ^7∏/6 radians into degrees.

MAKING THE SUBJECT 1

If A = BCQ make Q the subject of the formula.

Solution

A = BCQ

  A   =   BCQ

BC      BC

 A   =   Q

BC     

Hence   Q =      A 

                         BC   

TRY THIS………………..

If A = WXN.  Make X the subject of the formula.

ARITHMETICS 1

Evaluate 44 x 237 + 463 x 44

Solution

= 44 x 237 + 463 x 44

= 44 x (237 + 463)

= 44 x 700

= 30800

Hence 44 x 237 + 463 x 44 = 30800

TRY THIS………….

Evaluate 376 x 516 + 484 x 376.

SUM OF A GP 1

The sum of the 1st five terms of a geometrical progression is 484. If the common ratio is 3, find the 1st term.

solution

S₅ = 484, G₁ = ?, r=3, n=5

S_n = G₁(rⁿ-1)/r-1

               

S₅ = G₁(r⁵-1)/r-1

               

484= G₁(3⁵-1)/3-1

               

484= G₁(243-1)

                  2

2 x 484= G₁(242)

                  

968= 242 G₁

⁴ 968   =  G₁

  242

G₁ = 4

Hence the 1st term is 4.

TRY THIS……………..

The sum of the 1st seven terms of a geometrical progression is 381. If the common ratio is 2, find the 1st term.