Question

A leprechaun places a magic penny under a​ girl's pillow. the next night there are 2 magic pennies under her pillow. each night the number of magic pennies doubles. how much money will the girl have after 19 ​nights?

Answer 1

Answer: The girl will have $5242.88 after 19 nights.

Step-by-step explanation:

We know that exponential equation is given by :_

$y=Ab^x$                (1)

, where A= initial amount

b= Multiplicative rate of growth

x= Time period.

Given : A leprechaun places a magic penny under a​ girl's pillow. the next night there are 2 magic pennies under her pillow.

i.e. A= 1

Each night the number of magic pennies doubles.

i.e. b= 2

Put value of A and b in (1), we get

$y=(1)(2)^x$  

$y=(2)^x$  

Put x= 19 , we get

$y=(2)^{19}=524288$  

Hence, the number of pennies the girl will get after 19 nights = 524288

Since 1 dollar = 100 pennies

⇒ 1 penny = 0.01 dollar [Using unitary method , we divide both sides by 100]

⇒ Total money in dollars = $524288\times0.01=\ 5242.88$

Hence, the girl will have $5242.88 after 19 nights.

Answer 2

2^18 power = 262,144