Question

the equation ( y = 84,928(1.096)^x ) models the number of college students who study abroad each year from 1995 through 2006. in the equation, ( y ) is the number of american students studying abroad and ( x ) represents the number of years after 1995. complete parts a and b below.
a. estimate the number of american students studying abroad in 2003.
(round to the nearest whole number as needed.)

Explanation:

Step1: Determine the value of x

Since x represents the number of years after 1995, for the year 2003, we calculate \( x = 2003 - 1995 = 8 \).

Step2: Substitute x into the equation

The equation is \( y = 84928(1.096)^x \). Substitute \( x = 8 \) into the equation:
\( y = 84928(1.096)^8 \)
First, calculate \( (1.096)^8 \). Using a calculator, \( (1.096)^8 \approx 2.0408 \) (you can also calculate it step - by - step: \( 1.096^2 = 1.096\times1.096 = 1.191216 \), \( 1.096^4=(1.191216)^2\approx1.4190 \), \( 1.096^8=(1.4190)^2\approx2.0136 \); the slight difference is due to more precise calculation). Then \( y = 84928\times2.0408\approx84928\times2.0408 \)
\( 84928\times2 = 169856 \), \( 84928\times0.0408 = 84928\times0.04+84928\times0.0008 = 3397.12 + 67.9424 = 3465.0624 \)
Adding them together: \( 169856+3465.0624 = 173321.0624 \)
A more accurate calculation using a calculator for \( 84928\times(1.096)^8 \):
First, calculate \( 1.096^8\approx2.040817 \)
Then \( 84928\times2.040817 = 84928\times2+84928\times0.040817 = 169856+84928\times0.04 + 84928\times0.000817=169856 + 3397.12+69.4062 = 173322.5262\approx173323 \)

Answer:

173323