Question
Diane and her husband are each starting a saving plan. Diane will initially set aside
and then add
every month to the savings. The amount
(in
dollars) saved this way is given by the function
, where
is the number of months she has been saving.
Her husband will not set an initial amount aside but will add
to the savings every month. The amount
(in dollars) saved using this plan is given by the
function
.
Let
be total amount (in dollars) saved using both plans combined. Write an equation relating
to
. Simplify your answer as much as possible.
dollars) saved this way is given by the function
Her husband will not set an initial amount aside but will add
function
Let
Ask by Brooks Stephens. in the United States
Jan 23,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The total amount saved
is given by the equation:
Solution

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The Deep Dive
To find the total amount
saved using both Diane’s and her husband’s plans, we can combine their savings functions. The total savings is represented by the equation:
Substituting the functions for
and
:
Now, combine like terms:
So the total amount saved after
months is given by
.
Now we have a clear understanding of how their savings contribute over time.
Saving plans like this can teach great lessons about financial growth and how initial investments, combined with consistent contributions, can lead to substantial savings over time. A little planning goes a long way!
Both Diane and her husband are setting themselves up for success! In real life, having a savings plan can save you from those “oops” moments when unexpected expenses pop up. Regular contributions can make a difference, so consider setting one up for your financial goals!