The temperature of water in a tub at time t is modeled by a strictly increasing , twice differentiable function. At time = 0, the temperature of the water is 55 degrees Fahrenheit. The water is heated for 30 minutes, beginning at time = 0.
time = 0, 4, 9, 15, 20
temp = 55, 57.1, 61.8, 67.9, 71

I'm trying to write an equation to satisfy those points. I feel like it's exponential but I keep getting different answers

Question

The temperature of water in a tub at time t is modeled by a strictly increasing , twice differentiable function. At time = 0, the temperature of the water is 55 degrees Fahrenheit. The water is heated for 30 minutes, beginning at time = 0. 
time = 0, 4, 9, 15, 20
temp = 55, 57.1, 61.8, 67.9, 71

I'm trying to write an equation to satisfy those points. I feel like it's exponential but I keep getting different answers