Answer to Question #159136 in Algebra for Jan

Question

In each case, write an equation that models the situation described.

a) An antique is purchased for $5000 in 1990. It appreciates in value

by 3.25% each year.

b) A town had 2500 residents in 1990. It grew at a rate of 0.5% per

year for t years.

c) A single bacterium of a particular type takes one day to double.

The population is P after t days.

Answer 1

a) Let's say X is a year in which we want to know the value. The amount of years that has past from 1990 would be X-1990. Therefore the value would be equal to $5000\cdot(1+\frac{3.25}{100})^{X-1990}=5000\cdot(1+0.0325)^{X-1990}$ .

b) The amount of years that has past from 1990 would is t. Therefore the population would be equal to $2500\cdot(1+\frac{0.5}{100})^{t}=2500\cdot(1+0.005)^{t}$ .

c) The population is P, the time that has past in days is t and the population doubles each time. Therefore the population at t-th day is $P\cdot2^t=2^t\cdot P$