O EXPONENTIAL AND LOGARITHMIC FUNCTIONSEvaluating an exponential function with base e that models a rea...The number of bacteria P (tin a certain population increases according to the following function, where time t is measured in hours.0.16tP (i) 2700eFind the initial number of bacteria in the population and the number of bacteria after 8 hours.Round your answers to the nearest whole number as necessaryInitial number:bacteriaNumber after 8 hours:bacteria?X

Question
Asked Sep 24, 2019

See attachment

O EXPONENTIAL AND LOGARITHMIC FUNCTIONS
Evaluating an exponential function with base e that models a rea...
The number of bacteria P (t
in a certain population increases according to the following function, where time t is measured in hours.
0.16t
P (i) 2700e
Find the initial number of bacteria in the population and the number of bacteria after 8 hours.
Round your answers to the nearest whole number as necessary
Initial number:
bacteria
Number after 8 hours:
bacteria
?
X
help_outline

Image Transcriptionclose

O EXPONENTIAL AND LOGARITHMIC FUNCTIONS Evaluating an exponential function with base e that models a rea... The number of bacteria P (t in a certain population increases according to the following function, where time t is measured in hours. 0.16t P (i) 2700e Find the initial number of bacteria in the population and the number of bacteria after 8 hours. Round your answers to the nearest whole number as necessary Initial number: bacteria Number after 8 hours: bacteria ? X

fullscreen
check_circle

Expert Answer

Step 1

Given,

P(t) 2700e0.16t
help_outline

Image Transcriptionclose

P(t) 2700e0.16t

fullscreen
Step 2

Now to find the initial number of bacteria populations put t = 0 in the above equation, we get

Initial number of bacteria = P(0)
= 2700e0.16x0
= 2700e°
= 2700 x 1
= 2700
help_outline

Image Transcriptionclose

Initial number of bacteria = P(0) = 2700e0.16x0 = 2700e° = 2700 x 1 = 2700

fullscreen
Step 3

To find the number of bacteria after 8 hours p...

. The number of bacteria after 8 hours = P(8)
= 2700e0.16X8
2700e1.2
= 9710.927
29711
help_outline

Image Transcriptionclose

. The number of bacteria after 8 hours = P(8) = 2700e0.16X8 2700e1.2 = 9710.927 29711

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Functions