Question

The table shows the value of an account x years after the account was opened. Based on the exponential regression model, which is the best estimate of the value of the account 12 years after it was opened?
$8,910

$8,980

$13,660

$16,040

Answer 1

Answer:

Correct choice is B

Step-by-step explanation:

The equation of the exponential regression model is $y=a\cdot b^x.$

1. When x=0, $y=a\cdot b^0=a=5,000;$

2. When x=2, then

$y=5,000\cdot b^2=5,510\Rightarrow b^2=\dfrac{5,510}{5,000}=\dfrac{551}{500}=1.102,\ b=\sqrt{1.102}\approx 1.05.$

3. The equation of the function is $y=5,000\cdot (1.05)^x.$ Note that

• $y(5)=5,000\cdot (1.05)^5\approx 6,381\approx 6,390;$
• $y(8)=5,000\cdot (1.05)^8\approx 7,387\approx 7,390;$
• $y(10)=5,000\cdot (1.05)^{10}\approx 8,144\approx 8,150.$

Therefore,

$y(12)=5,000\cdot (1.05)^{12}\approx 8,979\approx 8,980.$

Answer 2

Answer:

Option B is correct

$8,980

Step-by-step explanation:

The equation of exponent  regression is given by:

$y=ab^x$ , x is the time

where, a is the initial amount and b is the growth factor

As per the statement:

Let y represents the account value.

Given table as shown the value of an account x years after the account was opened.

Enter the values for x into one list and the values for y into the second list.    

Now, graph the scatter plot as shown below in the attachment.

then, we get the equation of exponent regression:

$y = 4999.8 \cdot e^{0.0489x}$

We can write this as:

$y = 4999.8 \cdot (e^{0.0489})^x$

⇒$y = 4999.8 \cdot (1.05)^x$             ...[1]

We have to find the  best estimate of the value of the account 12 years after it was opened

Substitute x = 12 years in [1] we have;

$y = 499.8 \cdot (1.05)^{12}$

⇒$y = 4999.8 \cdot 1.7959$

Simplify:

y  ≈ $8979

Therefore,  the best estimate of the value of the account 12 years after it was opened is, $8980