It will take the bacteria population t = 16.30 to reach 15,000.
What is the exponential equation?
The exponential equation is given as [tex]\mathbf{\mathf{N_t = N_o e^{ct}}}[/tex] is being used to make an estimate in the scientific process such as:
- For the spread of bacteria,
- The growth of a population, or
- The time it takes a material to age regarding its' radioactivity.
From the parameters given:
[tex]\mathbf{\mathf{N_t = N_o e^{ct}}}[/tex]
where:
- N_t = Final population number at time (t)
- N_o = original population number
- e = natural e (constant)
- c = growth rate
- t = time
[tex]\mathbf{15000 = 50e ^{0.35 t}}[/tex]
[tex]\mathbf{\dfrac{15000}{50} =e ^{0.35 t}}[/tex]
[tex]\mathbf{300=e ^{0.35 t}}[/tex]
[tex]\mathbf{In(300)=0.35t}[/tex]
[tex]\mathbf{5.70378=0.35t}[/tex]
[tex]\mathbf{t=\dfrac{5.70378}{0.35}}[/tex]
t = 16.30
Learn more about exponential equations here:
https://brainly.com/question/12940982
