Question

Andrea invested $3,000 in an online currency. If the value of the currency increases at a rate of 14% per year, the situation can
be modeled using the equation A (t) = 3, 000(1.14)*, where A is the amount in the investment after t years. In 3 in
sentences, identify the key features of the graph and interpret the meaning of the data.

Answer 1

The graph has y-intercept A(0) = 3000 and, because the base 1.14 > 1, it is an upward-sloping exponential curve that grows without bound as t increases (with a horizontal asymptote A = 0 to the left). The factor 1.14 means the investment increases by 14% each year, so after 1 year A(1) = 3000(1.14) = 3420 and in general A(t) = 3000(1.14)^t. At that rate the investment will roughly double in ln(2)/ln(1.14) ≈ 5.3 years, so the value keeps rising and reaches about twice the original amount in a little over five years.