Help with an Algebraic model?

Attachment 23797 The shape of the curve of best fit suggests that the relationship between T and t is exponential. Se we assume that the algebraic model is - T=ka^t - where k and a are the constants to be determined.

c) Using the information provided calculate the values for k and a.

d) Hence find an expression for T.

e) Use your model from d) to predict the increase in the earth's temperature by the year 2060 above its 1860 value.





Also for the first part of the question I need help.

The Greenhouse Effect refers to the global warming due to increasing concentrations of certain gases in the atmosphere. Combustion of fossil fuels - coal, petroleum and natural gas - is the main way in which human societies contribute to overall increases in Greenhouse gases in the atmosphere. Forest clearing is also a factor and there are many others.
Formulating a Mathematical Model
Many factors contribute to the Greenhouse Effect. We must simplify this complex situation by making some assumptions about the variables. We will restrict ourselves to just two variables - an independent variable and dependent variable.
We define the variables as follows:
t =Number of years since 1860 (independent variable)
T = Rise in average over the 1860 value.
We can ignore all other variables.

a) What assumptions have we made? What other variables could be considered to make this model more accurate?






Thank You (Hi) Please share your working and try to explain your answer, it'd be much appreciated.



** On the graph the points are both from T and t as the graph shows the number of years since 1860 (t) and the rise in the average temperature (T)**

Not showing working, that's your job.

Your graph gives you several points that lie on the curve. So substitute them into T = k a^t and try to solve the two equations simultaneously for k and a.