Question

Norma received 1 penny on the first day of the month, and each day after that, she received triple the number of pennies that she received the day before. On what day of the month did Norma first receive over 10 million dollars on a single day?

Answer 1

20

Explanation:

APEX

Answer 2

note that this isn't a summation problem, it just wants to find on what day will she get 10,000,000 dollars in 1 day

convert that the pennies to make it easier (100 pennies=1 dollar so that's 1,000,000,000 or a billion pennies) (note that 1,000,000,000=10^9)

each day is 3 times of the other

first day is 1, 2nd is 1*3, 3rd day is 1*3*3, 4th day is 1*3*3*3, etc

hmm, so after n days, the number of pennies is
`1*3^(n-1)`

one long way is to keep dividing by 3 to find how many times we need to do that to find n

easier way is to do this:

1,000,000,000=
`3^(n-1)`

take ln of both sides

`ln(1,000,000,000)=ln(3^(n-1))`

`ln(10^9)=ln(3^(n-1))`

use properties of logarithms

`9ln(10)=(n-1)ln(3)`

divide both sides by ln(3)

`(9ln(10))/(ln(3))=n-1`

add 1 to both sides

`(9ln(10))/(ln(3))+1=n`

using your calculator we get 19.863=n

so after 19.863 days

but we need a whole number of days so round up to 20

20 days

it will be on day 20 of the month