Compound interest is a linear model because you earn interest on the current balance, which includes the initial balance plus previous interest.

Answer 1

linear is when the subtraction of consecutive outcomes divided by the variable amounts

are in a constant ratio,,,,,,,,,,m=constant=(y₂-y₁)/(x₂-x₁)

linear is based on the subtractive differences

look at simple interest, Q%=Q/100 per year,,,Principle=P,,, variable=t

t=0 y₁ amount=P

t=1 y₂ amount=P(1+Q/100)

t=2 y₃ amount=P(1+Q/100)²

(y₃-y₂)/(2-1)=PQ/100+P(Q/100)²

(y₂-y₁)/(1-0)=PQ/100

since (y₃-y₂)/(x₃-x₂)≠(y₂-y₁)/(x₂-x₁) simple interest is not linear growth

compound interest just makes it less linear

however, note: for equal intervals y₃/y₂=y₂/y₁=y_n+1/y_n=1+Q/100

which is indicative of exponential growth

exponential growth is when divisions of outcomes y_n+1/y_n

for equally consecutive variable increases are constant