Assume that a population size at time t is N(t) anf that N(t)=40*2^t , t >0 a)Find the population at time t = 0. b)Show that N(t) = 40e^(tln2) , t > 0 c)How long will it take until the population size reaches1000? [Hint:Find t so that N(t) = 1000]

Janiya Rose

Janiya Rose

Answered question

2022-08-07

Assume that a population size at time t is N(t) anf that N ( t ) = 40 2 t , t > 0
a)Find the population at time t = 0.
b)Show that N ( t ) = 40 e t ln 2 , t > 0
c)How long will it take until the population size reaches 1000? [Hint:Find t so that N(t) = 1000]

Answer & Explanation

Bridget Vang

Bridget Vang

Beginner2022-08-08Added 11 answers

a) N(t) at t=0
N ( 0 ) = 40 ( 2 0 )
= 40*1
= 40
b) Property of logarithms a = b log b a
hence 2 t = e ln 2 t
2 t = e t ln 2
40 2 t = 40 e t ln 2
N ( t ) = 40 e t ln 2
c) N(t) = 1000
40 2 t = 1000
2 t = 1000 / 40
2 t = 25
taking log to the base 10 both sides
log ( 2 t ) = log 25
t log 2 = log 25
t = ( log 25 ) / log 2
= 4.644
Jaxson Mack

Jaxson Mack

Beginner2022-08-09Added 4 answers

(a) t=0; therefore, N ( 0 ) = ( 40 ) 2 0 N ( 0 ) = ( 40 ) ( 1 ) N ( 0 ) = 40
(b) 40 e ln ( 2 ) t > 0 40 40 e ln ( 2 ) t > 0 40 e ln ( x ) = x 2 t > 0 t > 0
(c)N(t)=1000; therefore,
1000 = ( 40 ) ( 2 t ) 1000 40 = 2 t ln ( 1000 40 ) ln ( 2 t ) ln ( 1000 40 ) = ( t ) ln ( 2 )
t = ln ( 1000 40 ) ln ( 2 ) t = 4.64385619 t 4.6

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