Question

Joan won a multi-million dollar lottery. She decides to give $1000000 of her winnings to charity. Her plan is to give 1/2, or 2^-1 to charity in January, then give half of the remaining amount in February, half again in March and so on. a) What fraction remains after 6 months? b) what fraction remains after 12 months? c) Write a fraction as a power of 2 with a negative exponent. d) What amount is remaining at the end of the year?

Answer 1

Answer:

A) 1/64

B) 1/4096

C) 1/64 = 2^(-6)

D)$244.140625 left.

Step-by-step explanation:

We are told that Joan decides to give $1000000 of her winnings to charity.

Now in January she gave ½ of the winnings to charity.

Which means she gave out;

½ × 1000000 = $500000

So she has left; 1000000 - 500000 = $500000

In February, she gives out ½ of what she has left.

Thus, ½ × 500000 = $250000

So at end of February she has $250000 left

At the end of March, she will have left;

250000 × ½ = $125000

At end of April, she will have left;

125000 × ½ = $62500

At end of May, she will have left;

62500 × ½ = $31250

At end Of June, she will have;

31250 × ½ = $15625

At end of July, she will have; 15625 × ½ = $7812.5

At end of August, she will have;

7812.5 × ½ = $3906.25

At end of September, she will have;

3906.25 × ½ = $1953.125

At end of October, she will have;

1953.125 × ½ = $976.5625

At end of November, she will have;

976.5625 × ½ = $488.28125

At end of December, she will have;

488.28125 × ½ = $244.140625

A) At end of 6 months which is end June, she will have $15625 left.

Thus, fraction left out of initial money is; 15625/1000000 = 1/64

B) At end of 12 months which is end of December, she will have $244.140625 left.

Thus, fraction left out of initial money is; 1/4096

C) For option A, writing it as a power of 2 with a negative exponent.

First of all 64 = 8²

We know that 8 = 2³

Thus 64 = 2^(6)

Thus; 1/64 = 1/(2^(6)) = 2^(-6)

D)At end of the year which is end of December, she will have $244.140625 left.