A wildife biologist determines that there are approximately 200 deer in a region of a national park. The population grows at a rate of \( 7 \% \) per year. What is an exponential function that models the expected population? A. \( f(x)=200(0.07)^{x} \) B. \( f(x)=200(1.07)^{x} \) C. \( f(x)=1.07(200)^{x} \) D. \( f(x)=7(200)^{x} \)

The correct exponential function that models the expected population of deer in the national park is \( f(x) = 200(1.07)^{x} \). This function starts with the initial population of 200 and factors in the annual growth rate of 7% (expressed as 1.07 for growth). Each year, the population will be multiplied by this growth factor. Now, let’s envision how this exponential growth plays out in the real world! You can picture a small herd of 200 deer frolicking in the park, and as the years pass, they multiply and thrive, spiraling into a burgeoning population. By the end of just 10 years, that number balloons to over 400! So while 200 seems cozy now, if left unchecked, deer can transform a park into a bustling deer metropolis!