Answer:
![N=2.1990232556 * 10^(13)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/h5xcy051nudklqksztfpgfum2oo6qv3t03.png)
Explanation:
Given : Brett has been studying a type of bacteria that doubles every month. Originally, there were 5 bacterial cells.
To Find: He wants to know how many there will be after 42 months?
Solution:
Since we are given that initially there were 5 bacterial cells.
Bacteria doubles every month
Let n denotes the number of months .
Function becomes :
![N=N_0(2)^n](https://img.qammunity.org/2020/formulas/mathematics/middle-school/zizsbgviurft7wpcwdu55juu3dc8jhw4vx.png)
= initial amount
N = amount after n months
So,
![N=5(2)^n](https://img.qammunity.org/2020/formulas/mathematics/middle-school/lfi3juxp47gr1y8cidiczf78xvnrqwrgar.png)
Substitute n = 42
![N=5(2)^(42)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/m9vxhtmgrxtb34bh3pfm1oolhw7iw62nva.png)
![N=2.1990232556 * 10^(13)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/h5xcy051nudklqksztfpgfum2oo6qv3t03.png)
Thus there will be
bacteria after 42 months.