The situations that could be modeled by the function g(x) = 100 • (2)^x are:
1. A 100in. tall fruit tree doubles in height each year.
3. There are 100 bacteria in a culture. The amount doubles every 5 hours.
5. 100 wolves are reintroduced to Yellowstone National Park. Each year, the number of wolves double.
Consider the exponential function g (x) = 100 • (2)^x. Which of the following situations could be modeled by the function? Select all that apply.
A 100in. tall fruit tree doubles in height each year.
100 people are infected with a virus. Every day, 2 more people are infected.
There are 100 bacteria in a culture. The amount doubles every 5 hours.
There is $100 in a savings account. An additional $100 is added to the account every month.
100 wolves are reintroduced to Yellowstone National Park. Each year, the number of wolves double.
3 answers
explain
The function g(x) = 100 • (2)^x represents exponential growth, where the base 2 indicates that the quantity is doubling over time. The initial value of 100 in each case corresponds to the starting point of the growth.
1. In the case of a 100in. tall fruit tree doubling in height each year, the height is increasing exponentially with each year, which can be accurately represented by the exponential function.
3. When there are 100 bacteria in a culture and the amount doubles every 5 hours, this growth pattern can be modeled by the exponential function.
5. Similarly, with the reintroduction of 100 wolves to Yellowstone National Park and the population doubling each year, the growth can be mathematically described using the exponential function.
The other situations listed do not fit the exponential growth model for this particular function.
1. In the case of a 100in. tall fruit tree doubling in height each year, the height is increasing exponentially with each year, which can be accurately represented by the exponential function.
3. When there are 100 bacteria in a culture and the amount doubles every 5 hours, this growth pattern can be modeled by the exponential function.
5. Similarly, with the reintroduction of 100 wolves to Yellowstone National Park and the population doubling each year, the growth can be mathematically described using the exponential function.
The other situations listed do not fit the exponential growth model for this particular function.