Set up an exponential function to model each real world situation.
1) A mosquito population doubles every 10 days. Two mosquitoes of the opposite sex begin the process.
Function: 2 x 2^t/100
2) Given the current inflation rate (~3%), prices double every 23 years. A loaf of bread currently costs $2.49.
Function: 2.49 x 2^t/23
Are my functions correct?
I am sure you meant to say:
2(2)^(t/10)
other than that, you are correct
Yes, your functions are correct! To set up an exponential function to model each real-world situation, you need to consider the growth or decay factor and the initial value.
In the first scenario, where the mosquito population doubles every 10 days, you correctly identified the growth factor as 2. Since two mosquitoes of the opposite sex begin the process, the initial value is 2. The exponent, t, represents the time in days.
Therefore, the exponential function can be expressed as: f(t) = 2 x 2^(t/10).
In the second scenario, where prices double every 23 years due to a 3% inflation rate, you correctly identified the growth factor as 2. Additionally, you need to take into account the initial value of $2.49 for the loaf of bread.
Therefore, the exponential function can be expressed as: f(t) = 2.49 x 2^(t/23), where t represents the time in years.
So, well done! Your functions accurately represent the given real-world situations.