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Tim deposits money in a certificate of deposit account. The balance (in dollars) in his account t years after making
the deposit is given by T(t) = 1000(1.06)t for t ≥ 0
b. By what percent does the value of T(t) grow each year? Explain by writing a recursive formula for the
sequence T(1), T(2), T(3), etc.

Answer :

aaisrakh

Answer:

6%

Step-by-step explanation:

First, you need to know how to calculate the increase percentage of one quantity relative to another quantity. You need to use the following expression:

[tex]Percent.increase= \frac{new - original }{original}(100)[/tex]

For example, if a group of 50 students increased to 60 students from 2018 to 2019, what is the percentage increase of the number of students?[tex]percent.increase=\frac{60-50}{50}(100)=20 percent[/tex]

In order to calculate the percentage increase each year with the values of the recursive formula, we have to calculate T(1), T(2) and T(3):

[tex]T(1) = 1000(1.06)^{1}=1060\\T(2) = 1000(1.06)^{2}=1123.6\\ T(3) = 1000(1.06)^{3}=1191.016\\[/tex]

Now, the questions are: what is the increase percentage from T(1) to T(2) and from T(2) to T(3) (note that these results must be the same). Let's do the math:

[tex]increase.percent=\frac{T(2)-T(1)}{T(1)}(100)=\frac{1123.6-1060}{1060}(100)=6 percent\\increase.percent=\frac{T(3)-T(3)}{T(2)}(100)=\frac{1191.016-1123.6}{1123.6}(100)=6 percent[/tex]

In conclusion, T(t) increases 6% each year.

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