By setting the calorie intake formula equal to 2200, isolating the logarithm, and exponentiating both sides, we found that the person owns approximately 1.9 acres of land for an average intake of 2200 calories per day.
Note: This is an estimate based on the given model. Actual calorie intake can vary depending on various factors beyond land ownership.
Estimating Land Ownership for 2200 Calorie Intake
We're given the formula C(x) = 270 ln(x + 1) + 1915, which models the daily calorie intake of a person owning x acres of land in a developing country. We need to estimate the number of acres, x, for which the average intake is 2200 calories, C(x) = 2200.
Here's how we can solve this:
Set the equation equal to 2200:
C(x) = 2200 = 270 ln(x + 1) + 1915
Isolate ln(x + 1):
Subtract 1915 from both sides:
285 = 270 ln(x + 1)
Divide both sides by 270:
ln(x + 1) = 1.052
Solve for x: To get rid of the logarithm, we need to exponentiate both sides:
Calculate the value of the exponent:
≈ 2.879
Subtract 1 from both sides:
x = 1.879
Therefore, for an average intake of 2200 calories per day, the person owns approximately 1.9 acres of land.