Question

analyzing rates of change

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$$\begin{array}{|c|c|} \\hline \\text{years} & \\text{value (\\$)} \\\\ \\hline 1 & 5,250 \\\\ \\hline 2 & 5,512.50 \\\\ \\hline 3 & 5,788.13 \\\\ \\hline 4 & 6,077.54 \\\\ \\hline 5 & 6,381.42 \\\\ \\hline 6 & 6,700.49 \\\\ \\hline \\end{array}$$

the data in the table represents the value of a savings account at the end of each year for 6 years. the relationship between the increasing years and the increasing value of the account is exponential.

there is dropdown rate of change in an exponential relationship.

after each year, the value of the account is dropdown times as large as the previous year.

Explanation:

Analyze the rate of change in an exponential relationship

Using the Exponential Rate of Change knowledge point
An exponential function grows by a constant factor over equal intervals. This means that the ratio of consecutive terms is constant, representing a constant multiplicative rate of change rather than a constant additive rate of change (which characterizes linear functions). Therefore, the first dropdown menu must be filled with "a constant multiplicative".

Calculate the constant multiplier

Using the Exponential Rate of Change knowledge point

$$
LATEXBLOCK0
$$

The value of the account after each year is \(1.05\) times as large as the value the previous year.

Answer:

The data in the table represents the value of a savings account at the end of each year for 6 years. The relationship between the increasing years and the increasing value of the account is exponential.

There is <blank>a constant multiplicative</blank> rate of change in an exponential relationship.

After each year, the value of the account is <blank>1.05</blank> times as large as the value the previous year.