A blogger had 400 subscribers to her blog in January. The number of subscribers has grown by a factor of 1.5 every month since then. Write a sequence to represent the number of subscribers in the 3 months that followed.

Tyler says that the sequence 1, 1, 1, . . . of repeating 1s is not exponential because it does not change. Do you agree with Tyler? Explain your reasoning.

In 2000, an invasive plant species covered 0.2% of an island. For the 5 years that followed, the area covered by the plant tripled every year.

A student said, “That means that about half of the island’s area was covered by the plant in 2005!”

Do you agree with his statement? Explain your reasoning.

A square picture with a side length of 30 cm is scaled, using a photocopier, so that the side lengths are reduced to 60% of their previous length. The copy is then scaled by 60% again.

1. What is the side length of the second copy of the picture?
2. What is the side length of the picture after it has been scaled by 60% 4 times? Show your reasoning.

Find the real solution(s) to each of these equations, or explain why there is no solution.