Answer:
7. a. [tex]y=12000(2)^{x}[/tex] and b. 768,000.
8. [tex]y=4000(1.05)^{t}[/tex].
Step-by-step explanation:
We know that, the exponential model is given by [tex]a(1+b)^{x}[/tex], where a = initial amount, b = growth rate and x = time period.
7. We are given that the initial population of bacteria is 12,000.
Also, the culture of bacteria doubles each day.
a. So, the exponential model becomes [tex]y=12000(2)^{x}[/tex], where x is the number of days.
b. Now, the population of bacteria after 6 days is [tex]y=12000(2)^{6}[/tex] i.e [tex]y=12000 \times 64[/tex] i.e. [tex]y=768,000[/tex]
Hence, the population after 6 days is 768,000.
8. We have that the initial number of students in the class is 4000.
Also, the growth rate of students is 5% i.e. 0.05.
Therefore, the number of students graduating t years after 2008 are [tex]y=4000(1+0.05)^{t}[/tex] i.e. [tex]y=4000(1.05)^{t}[/tex].
