Respuesta :
9452
Explanation
an exponential function is given by:
[tex]\begin{gathered} y=a(b)^x \\ \text{where a is the initial amount} \\ b\text{ is the rate of change} \\ x\text{ is the time} \end{gathered}[/tex]so
Step 1
Set the equations
a) initial population = 2363
time=0
replace
[tex]\begin{gathered} y=a(b)^x \\ 2363=a(b^0) \\ 2363=a\cdot1 \\ 2363=a \end{gathered}[/tex]b) If the number of bacteria doubles every 157 minutes
[tex]\begin{gathered} (2363\cdot2)=2363(b^{157}) \\ (2363\cdot2)=2363(b^{157}) \\ 4726=2363b^{157} \\ \text{divide both sides by }2363 \\ \frac{4726}{2363}=\frac{2363b^{157}}{2363} \\ 2=b^{157} \\ 2^{(\frac{1}{157})}=(b^{157})^{\frac{1}{157}} \\ 1.00442471045\text{ =b} \end{gathered}[/tex]so, the function is
[tex]y=2363(1.00442471045)^x[/tex]Step 2
what will the population be 314 minutes from now?
Let
time=x =314
replace
[tex]\begin{gathered} y=2363(1.00442471045)^x \\ y=2363(1.00442471045)^{314} \\ y=2363\cdot4 \\ y=9452 \end{gathered}[/tex]therefore, the answer is
9452
I hope this helps you
