It is thought that a joke would spread in a school according to an exponential model N = 4 × (1.356)0.4t, t  0; where N is the number of people who have heard the joke, and t is the time in minutes after the joke is first told. (a) How many people heard the joke initially? (b) How many people had heard the joke after 16 minutes? There are 1200 people in the school.

A person puts $6,500 in a savings account. The bank pays 7% annual interest compounded quarterly. nt r A = P (1+ 5)" A = 6, 500 (1.0175)t

A painting sold for $246 in 1980 and was sold again in 1985 for $439. Assume that the growth in the value V of the collector's item was exponential. C a) Find the value k of the exponential growth rate. Assume V₂ = 246. (Round to the nearest thousandth.) b) Find the exponential growth function in terms of t, where t is the number of years since 1980. V(t) = c) Estimate the value of the painting in 2007. (Round to the nearest dollar.) d) What is the doubling time for the value of the painting to the nearest tenth of a year? years (Round to the nearest tenth.) e) Find the amount of time after which the value of the painting will be $6430. years (Round to the nearest tenth.)