pre calc question

Question

The area of an algae bloom is given by A(t)=100 e0.094t square feet, where t is measured in days. By what percentage does the area increase each day? Remember to give your answer as a percentage, and include at least three decimal places. 

Answer: The area increases by    % each day.

Answer 1

Hey Ashley. I decided to approach the problem in the following way:

Set kA(t)=A(t+1). We then solve for k, the scaling factor, and use this to determine the percent increase. First,

kA(t)=A(t+1) ⇒ k(100e^0.094t)=100e^0.094(t+1) = 100e^0.094t+0.094=100e^0.094te^0.094

⇒ k(100e^0.094t)=100e^0.094te^0.094 ⇒k=e^0.094

Now, k is a scaling factor. We see that k≈1.098559745. Thus there is an increase from A(t) to A(t+1) of approximately 9.8559745 percent.

Answer 2

.094 = 9.400% increase square feet daily

A = Pe^rt where t=time = days, r = % increase daily = 9.4%