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# Mathematics

Please show all woCarlos is blowing air into a soap bubble at the rate of 7 cm3/sec. Assuming that the bubble is spherical, how fast is its radius changing at the instant of time when the radius is 11 cm?
cm/sec.

How fast is the surface area of the bubble changing at that instant of time?
cm2/sec.

The Millers are planning to buy a home in the near future and estimate that they will need a 30 yr fixed-rate mortgage for \$120,000. Their monthly payment P (in dollars) can be computed using the following formula where r is the interest rate per year.

(a) Find the differential of P. (Do this on paper. Your teacher may ask you to turn in this work.)

(b) If the interest rate increases from the present rate of 5% per year to the following amounts between now and the time the Millers decide to secure the loan, approximately how much more will their monthly payment be?
5.2% per yr : \$
5.3% per yr : \$
5.4% per yr : \$
5.5% per yr : \$rk.

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