Question

The number n of college graduates in thousands after t years can be modeled by = 46 log10( +3). Let t = 0 represent 1985. a) How many college graduates were there in 2003? Round to the nearest thousand. b) During what year will there be 70,000 college graduates?

Answer 1

In 2003, there were approximately 152,000 college graduates. The year when there will be 70,000 college graduates is approximately 31 years after 1985.

Step-by-step explanation:

To find the number of college graduates in 2003, we can substitute t = 2003 in the given equation:

n = 46 log(2003 + 3)

n = 46 log(2006)

Using a calculator, we find that log(2006) ≈ 3.302

n = 46 * 3.302

n ≈ 151.892

Round to the nearest thousand, there were approximately 152,000 college graduates in 2003.

To find the year when there will be 70,000 college graduates, we set n = 70:

70 = 46 log(t + 3)

Divide both sides by 46:

log(t + 3) = 70/46

log(t + 3) ≈ 1.522

Now we need to solve for t. To do this, we can convert the logarithmic equation into an exponential equation:

t + 3 = 10^(1.522)

t + 3 ≈ 33.529

Subtract 3 from both sides:

t ≈ 30.529

Rounding to the nearest whole year, there will be approximately 31 college graduates in the year 31 after 1985.