The population of Smalltown in the year 1890 was 6,250. Since then, it has increased at a rate of 3.75% each year. • What was the population of Smalltown in the year 1915? • In 1940? • What will the population of Smalltown be in the year 2003? • When will the population reach 1,000,000 (to the nearest year) ?

year 1915 : 15,689 year 1940 : 39,381

t = 137.9 years

Step-by-step explanation:

Hi, to answer this question we have to apply an exponential growth function:

A = P (1 + r) t

Where:

p = original population

r = growing rate (decimal form)

t = years

A = population after t years

Replacing with the values given:

A = 6,250 (1 + 3.75/100) ^t

A = 6,250 (1 + 0.0375) ^t

A = 6,250 (1.0375) ^t

So, by the year 1915:

1915-1890 = 25 years passed (t)

A = 6,250 (1.0375) ^25

A = 15,689

by the year 1940:

1940-1890 = 50 years passed (t)

A = 6,250 (1.0375) ^50

A = 39,381

When will the population reach 1,000,000?. We have to subtitute A=1000000 and solve for t.

1,000,000 = 6,250 (1.0375) ^t

1,000,000 / 6,250 = (1.0375) ^t

160 = 1.0375^t

log 160 = log 1.0375^t

log 160 = (t) log 1.0375

log160 / log 1.0375 = t

t = 137.9 years