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)?

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

1915-1890 = 25 years passed (t)

A = 6,250 (1.0375)^25

A = 15,689

1940-1890 = 50 years passed (t)

A = 6,250 (1.0375)^50

A = 39,381

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

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step-by-step explanation:

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