Question

The growth of a certain species​ (in millions) since 1980 closely fits the following exponential function where t is the number of years since

1980.
A(t)=3400e⁰.⁰¹⁶⁶ᵗ
a. The population of the species was about 4024 million in 1990. How closely does the function approximate this​ value?

Answer 1

The exponential function A(t) provides a close approximation of the species population for the year 1990, with a calculated value of approximately 4013.7 million compared to the actual population of 4024 million.

Step-by-step explanation:

To determine how closely the exponential function A(t) = 3400e0.0166t approximates the population of a species in 1990, we substitute t = 10 (since 1990 is 10 years after 1980) into the function:

A(10) = 3400e(0.0166 × 10)

Calculating the value of A(10), we get:

A(10) = 3400e0.166 ≈ 3400 × 1.1805 ≈ 4013.7 million

The approximate population according to the exponential function for 1990 is 4013.7 million. This is very close to the actual population given, which is 4024 million. Therefore, the function provides a close approximation of the actual population.