A population of bacteria is growing according to the equation P(t)=850e0.19t Estimate when the population will exceed 1685. t=?

#e^(0.19t) #

2 Answers
Shiva Prakash M V
Feb 27, 2018

#t=1.56411 sec#

Explanation:

Given:
#P=850e^(0.19t)#

#P=1685#

#t=?#

#1685=850e^(0.19t)#

#1685/850=e^(0.19t)#

#1.982353=e^(0.19t)#

Taking logarithms

#ln1.982353=0.19t#

#0.297181=0.19t#

#0.19t=0.297181#

#t=0.297181/0.19#

#t=1.56411 sec#

Niranjana
Feb 27, 2018

The population will exceed 1685 when t = 3.5

Explanation:

Given : P(t) = #850e^(20.19t)#
To find: When P = 1685 t = ?
Solution: P(t) = #850e^(0.19t)#
1685 = #850e^(0.19t)#
#1685/850#= #e^(0.19t)#
1.98 = #e^(0.19t)#
#ln 1.98# = 0.19t
0.68 = 0.19t
t = 3.6
( you haven't mentioned about the unit of time )

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