The height of tree (m) is expected to increase exponentially. The height of tree after years is given by P(1) = 1.5e22.

(a) Calculate the lieight of tree (Correct to two decimal places) after years and complete the following table.

(b) Draw the graph for Height(m) against Time(year).

(c) Using the graph. find the time when the height of tree increases to 2 times.

To solve this problem, let’s go through each part step-by-step.

### (a) Calculate the height of the tree and complete the table.

The exponential growth of the tree’s height can be expressed as:
\[
P(t) = P_0 e^{kt}
\]
where:
- \( P_0 \) is the initial height of the tree,
- \( k \) is the growth rate,
- \( t \) is the time in years.

Given:
\[
P(1) = 1.5e^{22}
\]

Since it’s not clear from your input what values of \( t \) we need for the table, could you please confirm the specific years (values of \( t \))? I’ll proceed with calculations once I have these values.

---

### (b) Draw the graph for Height (m) against Time (year).

Once the table values are complete, I’ll plot a graph of height against time.

---

### (c) Using the graph, find the time when the height of the tree doubles.

The time at which the height of the tree doubles can be calculated by setting \( P(t) = 2P_0 \) and solving for \( t \). This will correspond to the point where the height reaches twice its initial value.

To proceed accurately:
1. Could you provide the initial height \( P_0 \) of the tree if it differs from \( 1.5 \)?
2. Confirm the time values needed for the table.

Once I have these details, I’ll complete each part accordingly. 

---

#### Would you like details on any part, or do you have any specific questions on this setup?

### Related Questions:
1. What is the formula for exponential growth and how is it derived?
2. How does exponential growth compare with linear growth over time?
3. Can exponential models be used for real-life predictions in natural systems like trees?
4. What factors could affect the rate of growth \( k \) for a tree?
5. How can one determine if a growth process truly follows an exponential model?

### Tip:
Always verify the values in exponential growth problems; small changes in parameters can lead to significant variations in results.

The height of tree (m) is expected to increase exponentially. The height of tree after years is given by P(1) = 1.5e22.

(a) Calculate the height of tree (Correct to two decimal places) after years and complete the following table.

(b) Draw the graph for Height(m) against Time(year).

(c) Using the graph, find the time when the height of tree increases to 2 times.

Learn how to solve exponential growth problems, such as calculating tree height over time using the model P(t) = P_0 e^(kt). The problem includes completing a table, plotting a graph, and determining the time when the tree's height doubles. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation