The relationship between the time a politician has been in office and his approval rating can be modeled by the equation y = –0.01x + 70, where x is his time in office in days and y is his approval rating as a percent. Which of these statements is true according to the model?

Because of absence of options, I have listed statements that are true; according to the model.

Step-by-step explanation:

To answer this, we find all possible explanations to the model. First, we know that:

X = time in office (in days)

Y = approval rating (in percentage)

The constant term in the model is 70

So the true statements that can be derived are:

(A) Y is inversely related to X. This is obvious because of the difference in sign of the coefficient of Y and that of X.

The coefficient of Y is +1

The coefficient of X is -0.01

Y has a positive coefficient while X has a negative coefficient.

The inverse relationship hence implies that the more days the politician spends in office, the less his percentage approval rating (and vice versa)!

Testing;

If X = 10 days, Y = 69.9%

If X = 20 days, Y = 69.8%

If X is 30 days, Y = 69.7%

(B) The rate at which approval rating drops is very slow; compared to the increase in number of days in office. A 10 day increase in number of days in office only results in a 0.1 or 10% decrease in percentage approval ratings.

(C) The longer a politician stays in office, the less his approval rating.

(D) The percentage approval rating is greatly influenced or increased by the constant term 70

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!

replication and blocking

step-by-step explanation: