a) The length of shadow is a function of the object’s height and the angle of the sun. The longest height of the object is when the sun’s angle to the Earth is very low or very high. Therefore, the height gets lower as the time passes and it gets higher again after the sun gets lower after 12’o clock. However, the shadow does not get longer after some point because the sun sets and there is no shadow until the sun rises again. This function has horizontal asymptote because the height of the shadow can approach 0, but it cannot be lower than 0.

b) Radioactivity level is one of examples of sequences because the radioactivity level decreases constantly. If we say that the radioactivity level decreases 5% every year, the amount of decreasing would be getting smaller and the level cannot reach 0. However, the level would be really close to 0 after many years. Therefore, this sequence would converge to 0.

C)  Bank account is one of examples of series, but not all the bank accounts are examples of the series. If a person puts money in the account, the account would pay probably 5% of interest to the person. As time passes, the account would pay more interest even if the percentage of the interest does not change because if the person does not withdraw money in the account, the account must have more money than the beginning. If there is more money, it means there would be more interest. The series will converge to infinity because as the money in the account gets bigger, the interest would get bigger, too. Therefore, the series would be converge to infinity.