The roosevelts and the jaspers live in the same city and pay the same sales
tax rate, and both families made $16,000 in taxable purchases last year, if the
roosevelts made $91.000 and the jaspers made 37000 last year, is the
sales tax in their city an example of a regressive tax?

Yes, because the Jaspers paid a higher percentage of their income in sales tax than the Roosevelts did.

Step-by-step explanation:

Regressive tax is a constant, instead of a percentage of income. Those with a lower income would pay a higher percentage of their income. Both families, irregardless of income, paid $16,000 in taxes.

APEX

Yes, because the Jaspers paid a higher percentage of their income in sales tax than the Roosevelts did.

Step-by-step explanation:

A regressive tax is one that collects a smaller percentage of the income as the person earns more. That is to say that at higher profit or higher income, the percentage of taxes that must be paid on the total tax base is lower.

In this way the poor are relatively more affected than the rich.

The Roosevelts made $91.000 (high income)

The Jaspers made $37.000 (low income)

But both paid the same sales tax rate of $16,000.

This type of tax does not have a redistribution effect of wealth. On the contrary, if it is a very high tax, it can accentuate inequality in a society.