A computer program enlarges the size of a file by a factor of after each complete cycle
MATHEMATICS · Multi-part · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions
Problem
A computer program enlarges the size of a file by a factor of 5 after each complete cycle. After (2u−3) cycles the enlargement factor is 52u−3. The same file is observed again after (u+5) cycles and is found to have exactly the same enlargement factor.
(i) Write an equation equating the two enlargement factors.
(ii) Solve this equation to find the value of u.
(iii) Using the value of u, determine after how many cycles the file first becomes 59 times its original size.