Assuming continuous compounding interest (this would probably be unsolvable if not), the usual formula to create this increase would be A=Pert or in other words, A=1100e0.07t ... but because the prompt says use half-life (decrease) or doubling (increase) we need to adjust our values. First let's find the time it would take your money to double. Double of A would be 2A, so double of 1100 would be $2200. So now our equation is 2200=1100e0.07t We will first divide both sides of the equation by 1100. Now we get 2=e0.07t . We will need to solve for t to get the "doubling time". Take the natural log of both sides. ln(2) = ln(e0.07t). Using the laws of logarithms, we can write the exponent of e as the coefficient of the logarithm and get: ln(2) = 0.07t[ln(e)]. Now evaluate the natural logs. ln(2)=0.693 rounded, and ln(e)=1 exact. So we get 0.693=0.07t. Divide both sides by 0.07 to achieve t=9.9. So it would take 9.9 or roughly 10 years to double your money. So now we can create the "doubling" formula: A=P(2)t/d where P is your original value, A is the value after so many years, d is your doubling time in years, and t is the actual elapse time. So the final answer should be:
A=1100(2)t/9.9
