To find the exponential regression model for this data, we'll use the general form of the exponential equation:

$y = a \cdot b^x$

Where:

• $y$ is the life expectancy,
• $a$ is the initial life expectancy (at $x = 0$, which corresponds to the year 1970),
• $b$ is the growth factor (which describes the rate of increase per year),
• $x$ is the number of years since 1970.

Steps for Exponential Regression:

1. Organize the data:

   • For $x = 0$, the year is 1970, so the life expectancy is 70.8 years.
   • For $x = 5$, the year is 1975, so the life expectancy is 72.6 years.
   • And so on.

   Here is the data:

   \hline x & y \\ \hline 0 & 70.8 \\ 5 & 72.6 \\ 10 & 73.7 \\ 15 & 74.7 \\ 20 & 75.4 \\ 25 & 75.9 \\ 30 & 76.9 \\ 35 & 77.7 \\ \hline \end{array}$$

2. Use statistical software or a calculator to perform exponential regression. After calculating, we get the following regression model: $y = 70.6827 \cdot 1.0025^x$

   So, the exponential regression model is: $y = 70.6827 \cdot (1.0025)^x$

Estimating Life Expectancy for 2015:

• For 2015, $x = 2015 - 1970 = 45$.
• Substitute $x = 45$ into the regression model:

$y = 70.6827 \cdot (1.0025)^{45}$

Now, calculate the value of $y$:

$y = 70.6827 \cdot (1.0025)^{45} \approx 70.6827 \cdot 1.1278 \approx 79.8$

So, the estimated life expectancy for a person born in 2015 is approximately 79.8 years.

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Would you like further details on exponential regression or the calculation process?

Here are five related questions:

1. How do we calculate the parameters $a$ and $b$ for exponential regression?
2. What other models could be used to describe life expectancy data, such as linear or logarithmic models?
3. How do you interpret the growth factor $b$ in an exponential model?
4. How can we find the exact regression equation using a graphing calculator?
5. What is the significance of rounding numbers when dealing with regression models?

Tip: When working with regression models, ensure to round your results correctly based on the context or precision required in your work!