Question

Graphing Exponential Functions questions 7 and 8

Answer 1

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

8.
`y=4000(1.05)^(t)`.

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 * 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)`.