Answer:
To find the y-intercept of the function h(x), we can use the given information that after 4 years, the tree was 7 feet tall. The y-intercept occurs when x (the number of years) is 0 because it represents the starting point or initial height of the tree. So, we have:
h(4) = 7
Now, let's use this information to calculate the y-intercept:
h(x) = mx + b
where m is the slope (rate of growth) and b is the y-intercept.
We can solve for b:
7 = m(4) + b
Since we know that the tree appears to grow at a constant rate, we can find the rate of growth (m) by looking at the change in height over the change in time:
m = (11 - 7) / (10 - 4) = 4 / 6 = 2/3
Now, we can find b:
7 = (2/3)(4) + b
7 = 8/3 + b
To isolate b, subtract 8/3 from both sides:
b = 7 - 8/3
b = 21/3 - 8/3
b = 13/3
So, the y-intercept of the function h(x) is 13/3, which is equivalent to 4 and 1/3 feet. Therefore, the correct answer is:
c. 4