If the change is at a constant rate (by a constant), the relationship is linear.
For example: The value of the account each month is 100 dollars bigger than the value in the previous month. If the initial value is 1,000 dollars, after 1 month it will be 1,000+100=1,100 dollars, after 2 months it will be 1,100+100=1,200 dollars etc. The function equation is y=1,000+100x.
If the change is by a percent from the initial value, the relationship is linear.
For example: The value of the account increases by 5 percent from the initial value each month. If the initial value is 1,000 dollars, the value of the account each month will increase by 50 dollars. After 1 month it will be 1,000+50=1,050 dollars, after 2 months it will be 1,050+50=1,100 dollars etc. The function equation is y=1,000+50x.
If the change is by a factor, the relationship is exponential.
For example: The value of the account each month is 2 times bigger than the value in the previous month. If the initial value is 1,000 dollars, after 1 month it will be 1,000*2=2,000 dollars, after 2 months it will be 1,000*2*2=4,000 dollars etc. The function equation is y=1,000*2x.
If the change is by a percent (from the previous value), the relationship is exponential.
For example: The value of the account increases by 5 percent (from the value in the previous month). If the initial value is 1,000 dollars, after 1 month it will be 1,000*1.05=1,050 dollars, after 2 months it will be 1,000*1.05*1.05=1,102.5 dollars etc. The function equation is y=1,000*1.05x.