Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by , where t is the number of years past 1960. The value of are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret . Round your answer to two decimal places, if necessary.

A) means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year.
B) means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year.
C) means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year.
D) means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month.
E) means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.

Question

Suppose the rate of change of total personal income I in the United States (in billions of dollars) can be modeled by

, where t is the number of years past 1960. The value of

are approximately $19,312.13 and $1,162.81 respectively which are been evaluated by using the arbitrary constant that is been evaluated by using the data point from 1960. Interpret

. Round your answer to two decimal places, if necessary.

A) means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be decreasing at a rate of $1,162.81 billion per year. 
B) means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be increasing at a rate of $19,312.13 billion per year. 
C) means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per year. 
D) means that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars and will be increasing at a rate of $1,162.81 billion per month. 
E) means that the model predicts that in 2020, the total personal income is predicted to be $1,162.81 billion dollars and will be decreasing at a rate of $19,312.135 billion per month.

Quizplus · Accepted Answer

The given expression represents the rate of change of total personal income in the United States, and it is evaluated to be around $19,312.13 billion in 2020, which means that the model predicts the total personal income to be $19,312.13 billion by the end of 2020. The value of the arbitrary constant evaluated using the data point from 1960 indicates that the rate of change will be increasing by $1,162.81 billion per year. Therefore, the correct interpretation of the expression 11ea984b_b18d_ca8f_9029_c1b0e8028816_TB4005_11 is that the model predicts that in 2020, the total personal income is predicted to be $19,312.13 billion dollars, and it will be increasing at a rate of $1,162.81 billion per year.

Suppose the Rate of Change of Total Personal Income I