2018 Individual Income Tax Rates
See https://www.irs.gov/pub/irs-pdf/n1036.pdf and https://www.irs.gov/pub/irs-pdf/i1040gi.pdf starting around page 31. The tax table starts on page 67. The rates (for $100,000+ incomes) are shown directly on the Tax Computation Worksheet which starts on page 79.
If a family earns $3,000 / month, or $36,000 per year, after the $24,000 deduction, their income for tax purposes is $12,000 and the tax is $1,203. If your income is under $24,000 of course there is no tax because for tax purposes your income is zero. If a family earns $60,000 / year then for tax purposes their income is $36,000 and their tax is $3,942.
Note that there is an additional standard deduction for elderly and blind taxpayers, which is $1,300 for tax year 2018. This amount increases to $1,600 if the taxpayer is also unmarried.