Using Logarithmic Regression to Fit a Model to Data

Due to advances in medicine and higher standards of living, life expectancy has been increasing in most developed countries since the beginning of the 20th century.
The table shows the average life expectancies, in years, of Americans from 1900–2010.

$$\begin{array}{ccccccc}\text{Year}& \text{1900}& \text{1910}& \text{1920}& \text{1930}& \text{1940}& \text{1950}\\ \text{Life Expectancy(Years)}& \text{47.3}& \text{50.0}& \text{54.1}& \text{59.7}& \text{62.9}& \text{68.2}\\ \text{Year}& \text{1960}& \text{1970}& \text{1980}& \text{1990}& \text{2000}& \text{2010}\\ \text{Life Expectancy(Years)}& \text{69.7}& \text{70.8}& \text{73.7}& \text{75.4}& \text{76.8}& \text{78.7}\end{array}$$

ⓐ Let $x$ represent time in decades starting with $x=1$ for the year 1900, $x=2$ for the year 1910, and so on. Let $y$ represent the corresponding life expectancy. Use logarithmic regression to fit a model to these data.
ⓑ Use the model to predict the average American life expectancy for the year 2030.

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Algebra and Trigonometry 2e · §6.8 Fitting Exponential Models to Data · Example 4