Using the exponential model given, the number of bacteria in the culture after 9 minutes after the observation began will be 4789
Given the exponential model :
- [tex] A(t) = 4000e^{0.02t} [/tex]
- [tex] A(t) = Number\:bacteria\:in\:the\:culture\:after\:t\:minutes [/tex]
- t = number of minutes after observation begins
The number of bacteria in the culture 9 minutes after the observation began can be calculated thus :
[tex]t = 9 \: minutes [/tex]
Substitute 9 for t in the exponential equation :
[tex] A(t) = 4000e^{0.02\times9} [/tex]
[tex] A(t) = 4000e^{0.18} [/tex]
[tex] A(t) = 4000 \times 1.1972173 [/tex]
[tex] A(t) = 4788.87 [/tex]
Therefore, the number of bacteria in the culture after 9 minutes will be about 4789
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