Question

The height of a plant over time is shown in the table below. using a logarithmic model, what is the best estimate for the age of the plant when it is 19 inches tall? plant height t, time in months h, height in inches 1 18 2 18.21 3 18.33 4 18.42 5 18.48 6 18.54 10 months 14 months 16 months 28 months

Answer 1

The age of the plant if the height of the plant is 19 inches is 28 months.

What is logarithmic regression?

The general equation for logarithmic regression is given by the formula,

y = a+b ln(x)

where y is the dependent variable, x is the independent variable, and a and b are the constants.

Let y be the height of the plant and x be the age of the plant.

If we plug in any two of the points in the equation, to get the value of a and b.

• x = 1 and y = 18

        $18=a+b\rm \ ln(1)\\\\18=a+0\\\\a = 18$

• x = 2 and y = 18.21

        $18.21=18+b\rm \ ln(2)\\\\0.21=b\ ln(2)\\\\b = 0.3$

Thus, the logarithmic expression represents the relationship between the age of the plant and the height of the plants is y=18+0.3 ln(x).

Now, if the height of the plant is 19, inches than the age of the plant is,

$y=18+0.3\rm\ ln(x)\\\\19 =18+0.3 ln(x)\\\\x = 28.03\approx 28$

hence, the age of the plant if the height of the plant is 19 inches is 28 months.

Learn more about Logarithmic Regression:

https://brainly.com/question/26907361

Answer 2

Answer:

28 months (d)

Step-by-step explanation:

its that because it is