this function, where t represents the time in weeks, models the height, in inches, of the peach tree…

Explanation:

Step1: Find the initial height

When (t = 0), (P(0)=3\ln(2\times0 + 3)-5=3\ln(3)-5\approx3\times1.0986 - 5=3.2958-5=- 1.7042). This means the peach - seed was planted below ground level. But we have no information about the avocado - tree's initial height, so we can't say if the avocado seed was planted at ground level or if the peach seed was planted closer to ground level.

Step2: Analyze long - term growth

As (t\to\infty), the function (P(t)=3\ln(2t + 3)-5) will increase without bound since the natural logarithm function (\ln(x)) increases as (x) increases. But we have no information about the avocado - tree's long - term growth, so we can't say if the peach tree will eventually be taller than the avocado tree.

Step3: Calculate the average rate of change

The average rate of change of a function (y = f(x)) from (x=a) to (x = b) is (\frac{f(b)-f(a)}{b - a}). For (P(t)=3\ln(2t + 3)-5), when (a = 2) and (b = 6): First, find (P(2)=3\ln(2\times2+3)-5=3\ln(7)-5\approx3\times1.9459-5 = 5.8377-5=0.8377). Second, find (P(6)=3\ln(2\times6 + 3)-5=3\ln(15)-5\approx3\times2.7081-5=8.1243 - 5=3.1243). The average rate of change from (t = 2) to (t = 6) is (\frac{P(6)-P(2)}{6 - 2}=\frac{3.1243 - 0.8377}{4}=\frac{2.2866}{4}=0.57165). Since we have no information about the avocado - tree's average rate of change between the 2nd and 6th weeks, we can't compare the two.

Since we have no information about the avocado - tree in the problem statement, we can't determine the truth of any of the statements.

Answer:

There is not enough information to determine which statements are true.