Question

Isabella saved 2 nickels today. If she doubles the number of nickels she saves each day, how many days, including today, will it take her to save more than 500 nickels?

Answer 1

Answer:

Step-by-step explanation:

Alright, lets gets started.

First day, she saves nickels = 2

As we know, she doubles the number of nickels she saves each day.

Means second day she saves nickels = $2*2 = 4$

Third day she saves nickels = $2*4 = 8$

Fourth day she saves nickels = $2*8=16$

Hence we have $2 + 4 + 8 + 16...$

It is like a geometric series, the sum of nickels she needs more than 500.

So, lets see how many days she will take to save 500 nickels first

Using the sum formula for geometric series

$s=\frac{a(1-r^n)}{(1-r)}$

where s is sum, r is multiplication factor, that is 2 in this case and a is first term of series that is 2 also

$500=\frac{2(1-2^n)}{(1-2)}$

Simplifying, dividing 2 in both sides

$250=\frac{(1-2^n)}{(1-2)}$

$250=\frac{(1-2^n)}{-1}$

Cross multiplying

$-250=1-2^n$

$2^n-1=250$

$2^n=251$

Taking log on both sides

$nlog2=log251$

$n=\frac{log251}{log2}=7.971$

It means it will take 8 days to save mmore than 500 nickels.   :  Answer

Hope it will help :)