Answer:
[tex]1000(.95)^h[/tex]
Step-by-step explanation:
[tex]h(t)=A \cdot B^t[/tex] is an exponential equation where A is the beginning amount and B is the rate that the population grows or dies.
So we start with 1000 bacteria, they are giving us A.
The bacteria population is decreasing because they are dying 5% each hour.
So that is after the first hour we have 1000-.05(1000) or 1000(1)-1000(.05)=1000(1-.05)=1000(.95).
We will keep multiplying by .95 per hour. 0.95 is the repeated factor.
That is the function is [tex]1000(.95)^h[/tex].
If you let h=0 which means 0 hours has happened, you will see the bacteria is 1000 as desired. 1000(.95)^0=1000(1)=1000.
