Math Problem Statement

A population grows according to an exponential growth model. The initial population is 202 and the population after one year is 295. Complete the formula where P is the population and n is the number of years.: P=202*(__)^n Round your answer to three decimal places.

Solution

To determine the base of the exponential growth model, we can use the following information:

  1. The initial population P0P_0 is 202.
  2. After one year, the population P1P_1 is 295.

The exponential growth formula is: P=P0×rnP = P_0 \times r^n where rr is the growth factor per year, and nn is the number of years.

Since we know P1=295P_1 = 295 when n=1n = 1, we can set up the equation:

295=202×r295 = 202 \times r

Solving for rr: r=295202r = \frac{295}{202} Calculating this value and rounding to three decimal places:

r1.46r \approx 1.46

So the completed formula is:

P=202×(1.46)nP = 202 \times (1.46)^n

Would you like additional details or have any questions?


Further Questions

  1. How does this exponential growth model change if the growth rate decreases over time?
  2. What would the population be after 5 years using this model?
  3. How would you interpret the growth factor r=1.46r = 1.46 in terms of annual growth rate?
  4. What other models besides exponential could represent population growth?
  5. How does exponential growth differ from linear growth?

Tip:

When interpreting exponential growth, a growth factor greater than 1 indicates an increase, while a factor less than 1 indicates a decrease over time.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Exponential Growth
Algebra

Formulas

Exponential growth formula: P = P0 * r^n

Theorems

-

Suitable Grade Level

Grades 9-11