Final answer:
Using the exponential growth formula and a continuous growth rate of 22% per day, it is calculated that a kudzu vine will take approximately 5.5 days to triple in length.
Step-by-step explanation:
To calculate how many days it will take for a kudzu vine to triple in length with a continuous growth rate of 22% per day, one can use the formula for exponential growth. Let L represent the final length, L0 the initial length, r the growth rate, and t the time in days.
The formula for continuous growth is L = L0ert, where e is the base of natural logarithms. To triple in length, we need L/L0 = 3. Setting up the equation we get 3 = e0.22t.
To find t, take the natural logarithm of both sides: ln(3) = 0.22t. Solve for t to get t = ln(3)/0.22 which approximately equals 5.5. Therefore, it will take about 5.5 days for the kudzu vine to triple in length.