Tabitha decided to start saving pennies for a stretch of two months and initially started with 2 pennies. A table showing the nu
mber 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.
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.
1 answer:
Answer:
- after week 7: 4374 pennies
- 486 pennies: after week 5
Step-by-step 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.
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