Sadie is saving for a new car. Below is the total amount of money in her savings account on the last day of each month. Show all
steps to find the mean amount of money Sadie saves each month. Round your answers to the nearest cent.
1 answer:
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Answer:
a) The recurrence formula is .
b) The general formula for the population of Tacoma is
.
c) In 2016 the approximate population of Tacoma will be 794062 people.
d) The population of Tacoma should exceed the 400000 people by the year 2009.
Step-by-step explanation:
a) We have the population in the year 2000, which is 200 000 people. Let us write . For the population in 2001 we will use
, for the population in 2002 we will use
, and so on.
In the following year, 2001, the population grow 9% with respect to the previous year. This means that is equal to
plus 9% of the population of 2000. Notice that this can be written as
.
In 2002, we will have the population of 2001, , plus the 9% of
. This is
.
So, it is not difficult to notice that the general recurrence is
.
b) In the previous formula we only need to substitute the expression for :
.
Then,
.
Repeating the procedure for we get
.
But we can do the same operation n times, so
.
c) Recall the notation we have used:
for 2000,
for 2001,
for 2002, and so on. Then, 2016 is
. So, in order to obtain the approximate population of Tacoma in 2016 is
d) In this case we want to know when , which is equivalent to
.
Substituting the value of , we get
.
Simplifying the expression:
.
So, we need to find the value of such that the above inequality holds.
The easiest way to do this is take logarithm in both hands. Then,
.
So, .
So, the population of Tacoma should exceed the 400 000 by the year 2009.