During a recent assembly at the elementary school my two daughters attend, a visitor asked how many children planned to go to college. Nearly every hand in the room shot up.

Colleges better hope those kids were being honest because, a decade from now when they are applying to school, the outlook for enrollment in higher education is dire. The number of high school graduates nationwide is projected to remain relatively flat for the next several years before rising a bit in the middle of next decade. But between 2026 and 2031 — a period of graduating classes that includes both of my daughters — the ranks of high school graduates are expected to drop by 9 percent.

Beyond the overall numbers shifting, high school graduating classes will become more diverse. Those classes will have fewer white students and more Hispanic students, according to demographers, and a greater range of academic abilities. Family incomes remain stagnant, so student financial need will increase. In other words, the decade ahead will be tumultuous for college enrollment.

Already, we’re beginning to see the impact of demographic changes in higher education. A survey released last week by the Chronicle of Higher Education found that 52 percent of private colleges and 44 percent of public colleges didn’t meet their enrollment goals this past fall.

“We’re an expensive product,” Kathryn Coffman, vice president and dean of admissions and financial aid at Franklin College in Indiana, told the Chronicle. “Now more than ever, outcomes are critical, and people want to know that the investment they’re making is going to result in something.”

For the last year, I’ve been studying projections regarding high school graduates nationwide. What I found is the country is heading into a lengthy period of significant differences in growth by region. The South and to a certain extent the West will account for nearly all the growth in the high school population over the next decade-plus. At the same time, the Northeast and Midwest — home to the highest density of colleges in the United States with a history of student migration between states —show a continued and steady decline.

The South, which accounted for one-third of the nation’s high school graduates around the turn of this century, will be responsible for nearly half at the peak of its growth in 2025. The West will account for 30 percent of the nation’s graduates by the midpoint of the 2020s.

As a result, the question I’ve been wrestling with is whether the next generation of college students will make the same choices as their predecessors and travel far distances to attend college. Evidence based on demographics and traditional student migration suggests they won’t. Even as more schools expand their search areas for admissions — Northeast universities, for instance, setting up shop in California —many indications suggest the market for students willing to get on a plane or drive several hours to college is not growing at the same rate.

The raw numbers are sobering. But then a new book landed on my desk a few weeks ago that put the figures in a new, and disturbing, light. In “Demographics and the Demand for Higher Education,” Nathan D. Grawe, an economics professor at Carleton College, in Minnesota, explores the overall decline in high school graduates in greater detail.

The enrollment forecast for regional colleges outside of the top 100 that tend to attract nearby students is grim.

As he notes early in the book, just because someone graduates from high school doesn’t mean she will go to college. The past two decades in higher education have been about expansion as the percentage of high school graduates going to college has increased even when high school enrollments plateaued. Higher education leaders have generally assumed that the college-going rate in the United States, now just shy of 70 percent, would continue to inch up. Few have considered it could move in the opposite direction.

In researching his book, Grawe created something he calls the “Higher Education Demand Index.” It attempts to adapt population trends into college-attendance forecasts, using federal education data to estimate the probability that different populations from different cities and states will go to college.

“Unless something unexpected intervenes, the confluence of current demographic changes foretells an unprecedented reduction in postsecondary demand about a decade ahead,” Grawe writes.

The overall number of high school graduates, he argues, is not sufficient in determining the future for colleges. For the most part, higher education is a local market. Most students, especially those with average academic records, go to schools close to home that have a reputation for attracting close-by applicants. Far fewer potential students means these regional schools are likely to struggle to fill seats.

Meanwhile, demand for elite colleges, those in the top 50, will remain strong nationwide.

According to Grawe’s demand index, several historically large markets of students, such as New York, Philadelphia and Boston, will post “dramatic losses of 15 percent or more” in college-going students. Overall, he estimates that four-year colleges nationwide in just one four-year period at the end of the 2020s stand to lose almost 280,000 students.

Not all schools will be affected equally, Grawe argues. Elite colleges— those ranked in the top 50 in U.S. News & World Report nationally — will have about half the drop-off in student demand as those outside the top 100 because household brand names attract students willing to travel far distances.

That presents interesting opportunities for those schools ranked 50 to 100, Grawe writes, because they could benefit from a spillover of students who can’t get in to top 50 schools (historically, the top schools haven’t expanded the number of spots to accommodate demand).

The consequences of what is about to happen will have an impact on schools and applicants. For a few schools in certain pockets of the country, it certainly means closure. While we’re unlikely to see massive numbers of colleges going out of business — just look at the turmoil that surrounded the unsuccessful campaign to close Sweet Briar College in 2015 — many colleges will need to merge or form deeper partnerships with schools in equally tough situations.

For students, the changes in demand will mean even more competition to get them to enroll. If schools can afford it, students with solid academic records and the means to pay something toward tuition are likely to get showered with financial incentives. So for parents such as me lucky enough to have kids born in the middle of the demographic trough that arrives at the end of the next decade, perhaps saving for higher education won’t be so worrisome as it sometimes seems.