Answer: The girl will have $5242.88 after 19 nights.
Step-by-step explanation:
We know that exponential equation is given by :_
[tex]y=Ab^x[/tex] (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
[tex]y=(1)(2)^x[/tex]
[tex]y=(2)^x[/tex]
Put x= 19 , we get
[tex]y=(2)^{19}=524288[/tex]
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 = [tex]524288\times0.01=\$5242.88[/tex]
Hence, the girl will have $5242.88 after 19 nights.
