Doubling and time

Question

Suppose you discover a magical U.S. dime (10 cent piece) that has the power to double (in quantity) each day when placed in fertile soil. After being planted in the soil for one day you now have 2 dimes, after two days you have 4 dimes, after three days you have 8 dimes, and so on. What is the dollar value of the dimes after 29 days?

 

(Round to the nearest dollar and do not use commas.)

Answer 1

This is a simple exponential equation of the form y=ab^x.  a is your initial condition, which in this case is the .10 .  Your b is the growth factor, which is the 2.

 

• y=.01(2)^x
• y(29)=.1(2)²⁹
• y(29)=.1*536870912
• y=53687091.20
• y=$53687091 to the nearest dollar
• y=$53,687,091 (Not sure why you don't want the commas!)