Question

Tabitha decided to start saving pennies for a stretch of two months and initially started with 2 pennies. A table showing the number of pennies she saved each week for the first three weeks is shown.

Use the exponential pattern in the table to complete the statements.

After 7 week, Tabitha saved _____ pennies.

When there are a total of 486 pennies, ____ weeks have passed.

Answer 1

• after week 7: 4374 pennies
• 486 pennies: after week 5

Explanation:

The sequence values have a first term of 6 and a common ratio of 3, so can be described by the formula ...

an = 6·3^(n-1)

This can be rearranged to ...

an = 2·3^n

__

When n=7, the value is ...

a7 = 2·3^7 = 4374 . . . . pennies saved after 7 weeks

__

To find when there are 486 pennies saved, we can solve the equation ...

486 = 2·3^n

243 = 3^n

log(243) = n·log(3) . . . . . . . take the logarithm

log(243)/log(3) = n = 5 . . . . divide by the coefficient of n

Tabitha will have saved 486 pennies after 5 weeks.