Exponential Growth/Decay

Question

In 2012, there were about 6.26​ billion cell phone subscribers in the world. During the next 5 years, the number of cell phone subscribers increased by about 4% each year.

a. Write an exponential model that represents the number of cell phone subscribers Y​ (in billions) T​ years after 2012.

Use your model to estimate the number of cell phone subscribers in 2016. Round your answer to two decimal places.

b. Use your model to estimate when the number of cell phone subscribers was about 7 billion. Round your answer to the nearest whole year.

Answer 1

the base is 1.04 (for four years only) per the given

c(t)=6.26*1.04^t ,,,,t in years,,,,0≤t≤4

c=7

take ln of both sides and move exponent to multiplier

ln(7)=ln(6.26)+t*ln(1.04)

t=[ln(7/6.26)]/ln(1.04)

same as t=[ln(7)-ln(6.26)]]/ln(1.04)

Answer 2

A(T) = 6.26(0.96)^T

A(4) = 6.26(0.96)⁴

7 = 6.26(0.96)^T