Question

The table shows the balance of a money market account over time. Write a function that represents the balance y

(in dollars) after t years.

Year, t Balance
0 $200
1 $230
2 $264.50
3 $304.18
4 $349.80
5 $402.27





































The value of a boat is $23,400. It loses 8% of its value every year. Write a function that represents the value y
(in dollars) of the boat after t years.

Answer 1

y = 200·1.15^t The required function is y=1.047t + 199.12

Explanation:

The ratio from one year to the next is 1.15, so the balance is a geometric sequence. Since t starts at zero, we can write the balance (y) after t years as ...

y = initial value · (common ratio)^t

y = 200·1.15^tThe given table shows the balance of a money market account over time.

Time (t) Balance(y)

0 200

1 210

2 220.5

3 231.53

4 243.1

5 255.26

The function that represents the balance y(in dollars) after t years is linear regression line, because the value of y increased linearly.

The linear regression function is defined as

Where,

Put the values from the below table in the above formulas.

The value of b is 11.047 and the value of a is 199.12. Here, the variable is t.

Therefore the required function is the anser up top