Question

In a village, the cases of a particular infectiousdisease have been exponentially decreasing ata rate of 90% per year since the people startedreceiving the vaccine. If there were 100 casesin the village to start with, predict the numberof cases after 3 years.

Answer 1

0.1 cases

Step-by-step explanation:

rate of decrease = 90%

initial amount = 100 cases

Since the decrease is exponential, we will apply exponential formula:

`\begin{gathered} y=a(1-r)^t \\ \text{where r = rate = 90\%} \\ a\text{ = initial amount = 100} \\ t\text{ = time = 3 years} \\ y\text{ = amount after a specified year} \end{gathered}`

Substitute the values into the formula:

`\begin{gathered} r\text{ = 90\% = 0.90} \\ y=100(1-0.90)^3 \\ y=100(0.1)^3 \end{gathered}`
`\begin{gathered} y\text{ = 100}(0.001) \\ y\text{ = 0.1} \end{gathered}`

Hence, the number of cases after 3 years is 0.1