Question

Starting in the year 1800, the population of the United States was recorded until the year 2000. The data is summarized below with a linear function and an exponential function to model the data.
Linear Function: f(x) = 1.363x - 35.2

Exponential Function: f(x) = 7.8 * 1.02^x

Use the linear function and calculate the predicted value and residual value for 1880. Then use the exponential function to calculate the predicted and residual value for 1920.
Select all answer choices that are correct.


b = -23.64
a = 73.84
a = 12.579
b = 73.84
c = 83.97
d = 21.73
c = -23.09

Answer 1

Answer:

$a = 73.84$, $b = -23.64$, $c = 83.97$, $d = 21.73$

Step-by-step explanation:

1880:

The predicted value is:

$f(80) = 1.363\cdot (80) - 35.2$

$f(80) = 73.84$

The residual value is:

$\Delta f = 50.2 - 73.84$

$\Delta f = -23.64$

1920:

The predicted value is:

$f(120) = 7.8 \cdot 1.02^{120}$

$f(120) = 83.97$

The residual value is:

$\Delta f = 105.7 - 83.97$

$\Delta f = 21.73$

Answer 2

Answer:

Step-by-step explanation: