Exponential Growth and Decay A=A_0e^{kt} Logistic Growth Model A=\frac{e}{1+ae^{-bt}} Newton`s law of

Lennie Davis

Lennie Davis

Answered question

2022-01-19

Exponential Growth and Decay A=A0ekt
Logistic Growth Model A=e1+aebt
Newton`s law of cooling T=C+(T0C)ekt

Answer & Explanation

Debbie Moore

Debbie Moore

Beginner2022-01-19Added 43 answers

The explicit form of the exponential growth model is defined as A(t)=A0ekt.
Where, A(t) denotes the population at any time t, A0 represents the initial population, k indicates the growth rate of the population and t denotes the number of years.
Let t be the number of years after 2000. So, the corresponding value of t for the year 2000 is t=0.
Substitute 0 for t, 6.04 for A(0), 50 for t and 10 for A(50) in the exponential growth model, and solve the system of equations, to determine the values of A0 and k.
A(t)=A0ekt
A(0)=A0ek(0)
6.04=A0
A(50)=A0ek(50)
10=6.04e50k
106.04=e50k
ln(1.6556)=ln(e50k) =50k ln(1.6556)50=k
0.0101k
Substitute 6.04 for A0 and 0.0101 for k in the exponential model A(t)=A0ekt to obtain the required function.
A(t)=A0ekt
=6.04e0.0101t Hence, the required exponential growth function is A(t)=6.04e0.0101t

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