Respuesta :
Answer:
Part A.
[tex]P=1200(1.1)^t[/tex]Part B
Year Money deposited
2006 1200
2010 1756.92
2014 2572.31
2018 3766.11
2022 5513.97
Explanation:
Since the saving of each year is increasing by 10%, we can describe the situation with an exponential growth formula:
[tex]P=P_0(1+r)^t[/tex]Where P0 is the initial amount, r is the growth rate and t is the number of years after 2006. So, replacing P0 by 1200 and r by 10%, which is equivalent to 0.1, we get:
[tex]\begin{gathered} P=1200(1+0.1)^t \\ P=1200(1.1)^t \end{gathered}[/tex]Then, to calculate the money deposited in 2010, 2014, 2018, and 2022, we need to replace t by 4, 8, 12, and 16 respectively. So, for each year, we get:
[tex]\begin{gathered} P=1200(1.1)^4=1756.92 \\ P=1200(1.1)^8=2572.31 \\ P=1200(1.1)^{12}=3766.11 \\ P=1200(1.1)^{16}=5513.97 \end{gathered}[/tex]Therefore, we can complete the table as:
Year Money deposited
2006 1200
2010 1756.92
2014 2572.31
2018 3766.11
2022 5513.97
