Question

Considering the population P, of Porcupines increases according to the equation P=1,876e^{rt}, where t is the time in years, and r is the rate of growth. Which of the below equations solve for r?

Answer 1

Answer: ln(p/1,876) /t

Step-by-step explanation:

given,

p=1,876e^{rt}

or, p/1,876 = e^{rt}

applying ln both side,

ln(p/1,876) = ln[e^{rt}]

as we know that,

ln e =  1;

or, ln(p/1,876) = rt *1

therefore, r =  ln(p/1,876) /t

Answer 2

Given:

Considering the population P, of Porcupines increases according to the equation P=1,876e^{rt}, where t is the time in years, and r is the rate of growth.

To find:

Which of the below equations solve for r?

Solution:

From given, we have,

Considering the population P, of Porcupines increases according to the equation P = 1,876e^{rt} ......(1)

where t is the time in years, and r is the rate of growth.

applying log on both sides of the equation (1), we get,

ln P = ln [1,876 × e^{rt} ]

ln P = ln 1,876 + rt

ln P - ln 1,876 = rt

ln P - 7.5368 = rt

r = (ln P - 7.5368)/t

∴ The equation r = (ln P - 7.5368)/t solve for r