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The rat population in a major metropolitan city is given by the formula n(t)=67e^0.035t where t is measured in years since 1994 and n(t)ismeasured in millions.

What was the rat population in 1994?
 
What is the rat population going to be in the year 2005?
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3 Answers

n(t) = 67e0.035t
 
In 1994 the rat population was 67,000,000 because any number times e0 = that number (i.e. e0 = 1)
 
The year 2005 was 11 years after 1994, so t = 11 years.
 
n(t) = 67*[e(0.035)(11 years)]
 
n(t) = 98.5 million.
Assuming the initial rat population was 67 million, simply plug in 11 for t, so:
 
2005-1994 = 11; Eleven years have passed.
0.035 * t = 0.035 * 11 = 0.385;
n(11) = 67 * e(0.035*11)
n(11) = 67 * e0.385 = 67 * 1.46961 = 98.4641 (million)
 
1.) In windows calculator, use View>Scientific view
2.) For ex use [Inv]. This changes the [ln] button to [ex].
3.) Multiply by 67.
 
.385 [Inv][ex] or [Inv][ln] or [Inv][log] on your calculator, then times 67.
 
e = 2.7182... > 1. So with a positive exponent, the result will also be >1. The more years pass, the greater the exponent,and the greater the result (and number of rats) will be. When you multiply by a number greater than one, the result will always be a bigger number.
Before 1994, n(0) = 67 
In year 1994, n(1) = 67e0.035 ≈ 67 * 1.03562 ≈ 69.386520
In year 2005, n(12) = 67e0.035*12 ≈ 67 * 1.521962 ≈ 101.9714242

The rat population in 1994 was ≈ 69,386,520

The rat population in 2005 going to be ≈ 101,971,424