6.05 Linear and exponential models
Interactive practice questions
During a sudden bacterial outbreak, scientists must decide between two anti-bacterial treatments that are currently being trialed to try to control the outbreak. In the laboratory, they apply Treatment A and Treatment B to two samples of the bacteria, each containing $200$200 microbes. They keep track of the number of microbes in each sample. The table shows the results.
| Number of hours ($t$t) | $0$0 | $3$3 | $6$6 | $9$9 |
|---|---|---|---|---|
| Number of microbes using Treatment A | $200$200 | $215$215 | $230$230 | $245$245 |
| Number of microbes using Treatment B | $200$200 | $600$600 | $1800$1800 | $5400$5400 |
Which treatment causes the number of microbes to increase at a linear rate?
A
B
By what amount is the number of microbes increasing each hour using Treament A?
Which treatment will better control the number of microbes?
A
B
The table shown below represents the revenue (in thousands of dollars) over time, of two new shoe companies- Foot Swag, $F\left(x\right)$F(x) and Sweet Kicks $K\left(x\right)$K(x).
A linear function and exponential function have been drawn on the same coordinate plane.
Nadia is considering two different career options.
She could accept a job with Kord Enterprise that has offered her an income of $\$125000$$125000 for the first year, and a projected income increase of $\$34000$$34000 each year after that.
Alternatively, she can start her own business, where she estimates her initial annual income to be $\$40000$$40000 for the first year, increasing by $40%$40% each year after that.