A biologist is studying a group of 75 mice whose population triples each year. The mice population, `M`, is given by the equation `M\left(t\right)=75\left(3\right)^{ t}` where `t` is time in years.

An initial investment of $100 is now valued at $150. the annual interest rate is 5%, compounded continuously. the equation 100e0.05t = 150 represents the situation, where t is the number of years the money has been invested. about how long has the money been invested? use your calculator and round to the nearest whole number. years

Which of the following would be a good name for the function that takes the weight of a box and returns the energy needed to lift it?

In each diagram, line p is parallel to line f, and line t intersects lines p and f. based on the diagram, what is the value of x? ( provide explanation)