Question

A population grows according to an exponential growth model. The initial population is P ₀=14, and the growth rate is r=0.4. Then: P ₁​ = P ₂ = ​ Find an explicit formula for P ₙ ​ . Your formula should involve n. Pₙ ​ = Use your formula to find P ₉ ​ P ₀ ​ = Give all answers accurate to at least one decimal place

Answer 1

The population growth can be represented by the equation Pₙ = P₀ * e^(r*n). For initial population P₀ = 14 and growth rate r = 0.4, the equation becomes Pₙ = 14 * e^(0.4*n). To find P₉, substitute n with 9 and calculate the expression.

Step-by-step explanation:

The population growth can be modeled using the formula Pₙ = P₀ * e^(r*n), where:

• Pₙ is the population at time n,
• P₀ is the initial population,
• e is the base of natural logarithms,
• r is the growth rate, and
• n is the number of growth periods.

Given P₀ = 14 and r = 0.4, the formula becomes Pₙ = 14 * e^(0.4*n)

To find P₉, we substitute n with 9: P₉ = 14 * e^(0.4*9). Calculate this expression to get the population at time 9, give your answer to at least one decimal place.

Learn more about Exponential Growth