Invasive species often experience exponential population growth when introduced into a new environment. Zebra mussels are an invasive species that have recently made their way into midwestern lakes. In about six months, a zebra mussel population quadruples in size. Suppose 10 zebra mussels are newly introduced into a local lake. Find a function Z(t) that models the population of zebra mussels t years after they have been introduced. Use the function to determine how many zebra mussels there will be in 15 months. Use the function to determine how many months will pass before the lake has one million zebra mussels.

Arandomized controlled trial is designed to evaluate the effect of metoprolol in patients with heart failure. while preparing for statistical analysis, the researcher reviews some common types of statistical errors. which of the following statements is true regarding a type i error in a clinical study? a. the study is not significantly powered to detect a true difference between study groups. bthe null hypothesis is true but is rejected in error. c. the null hypothesis is false but is accepted in error. d. type i error is also known as beta and is usually 0.1 or 0.2. e. type i error depends on the study's confidence interval.