In Canada, federal income tax is calculated as follows: there is a 15% tax on income up to$49 200. The next$49 200 of income is taxed at a rate of 20.5% (on the portion of income over$49 200 up to$98 400). The next$53 939 of taxable income (over$98 400 and up to$151 978) is taxed at 26%. For example, an income of$100 000 would have the first$49 200 taxed at a rate of 15%, the next 49 200 taxed at a rate of 20.5% and the remaining$1600 taxed at a rate of 26%.

a) Write a piecewise function for the tax rate

R(as a percent) as a function of taxable income

I(in dollars).

b) How much tax would be calculated on a taxable income of $140 000?