Question

A dust bunny gathers dust at a rate of 11% per week. The dust bunny, Alfred, originally weighed 0.7 ounces. Write an equation that represents the weight of Alfred at a given time. Use t for weeks and w for the weight of the dust bunny. Using this equation, what is the weight of the dust bunny after 7 weeks?

Answer 1

Alfred is 0.7 ounces at the beginning.
After one week had passed, he is 11% larger. 0.7 * 1.11
After two weeks, the dust bunny's size is once again 11% larger.
0.7 * 1.11 * 1.11, or 0.7 * 1.11².

From here you can see that each week the dust bunny's size multiplies by 1.11. (1 whole plus 11 percent) How many times it is multiplied can be expressed with exponents.

$w = 0.7*1.11^{x}$