A population, 𝑃(𝑡) (in millions) in year 𝑡, increases exponentially. Suppose 𝑃(6)=21 and 𝑃(15)=31.

Question

A population, 𝑃(𝑡)P(t) (in millions) in year 𝑡t, increases exponentially. Suppose  𝑃(6)=21  P(6)=21  and  𝑃(15)=31 P(15)=31.

 

a) Find a formula for the population in the form 𝑃(𝑡)=𝑎𝑏𝑡P(t)=abt. Enter the values you found for a and b in your formula in the blanks below. Round your values to 4 decimal places.

    𝑎=    a=      𝑏=    b= 

 

b) If 𝑃(𝑡)=𝑎𝑒𝑘𝑡P(t)=aekt, what is the value of 𝑘k in your formula.

    𝑘=    k=  (round to 4 decimal places)

Answer 1

21 = pe^6k

31 = pe^15k

1.47619 = e^9k

ln 1.47619 = 9k

Cank you solve for k and answer?