Question

Graphing Exponential Functions questions 7 and 8

Answer 1

Answer:

7. a. $y=12000(2)^{x}$ and b. 768,000.

8. $y=4000(1.05)^{t}$.

Step-by-step explanation:

We know that, the exponential model is given by $a(1+b)^{x}$, 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 $y=12000(2)^{x}$, where x is the number of days.

b. Now, the population of bacteria after 6 days is $y=12000(2)^{6}$ i.e $y=12000 \times 64$ i.e. $y=768,000$

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 $y=4000(1+0.05)^{t}$ i.e. $y=4000(1.05)^{t}$.