Question

A population is increasing according to the exponential function defined by y = 3e^.04x, where y is in millions and x is the number of years. Which of the following should be done in order to answer the question "When will the population reach 4 million?"
A. Solve 3e^.04x=12
B. Evaluate y = 3e^.04x(4).
C. Evaluate y = 3e^.04x(1/4)
D. Solve 3e^.04x= 4.

Answer 1

Answer:

D. Solve 3e^0.04x= 4.

Step-by-step explanation:

Given the population increasing according to the exponential function defined by y = 3e^0.04x, where y is in millions and x is the number of years, to determine when the population will reach 4 million, the following steps must be carried out.

Since y is in millions, we will first substitute y = 4 into the modeled equation as shown;

4 =  3e^0.04x

Therefore to calculate x, we need to solve the expression 3e^0.04x = 4 for the value of x and this is arrived at by simply substituting y = 4 into the given equation.

To get x;

3e^0.04x = 4

e^0.04x  = 4/3

taking the ln of both sides

lne^0.04x = ln1.333

0.04x = 0.287

x = 0.287/0.04

x≈ 3.59 years