Algebra 1 Common Core Student Edition, Grade 8-9

Pr o b l em 3 M odel i ng Exp o nent i al Decay

Will the pressure ever
be negative?
No. The range o f an
exponential decay
fu n c tio n is all p o sitive
real numbers. The graph
of an exponential decay
function approaches but
does not cross the x-axis.

Physics Ihe kilopascal is a unit of measure for atmospheric pressure. The

atmospheric pressure at sea level is about 101 kilopascals. For every 1000-m increase

in altitude, the pressure decreases about 11.5%. What is the approximate pressure at

an altitude of 3000 m?

Relate

Define

y = a • bx Use an exponential function.

L e tx = th e altitude (in th o u sa n d s of m eters).

L ety = th e atm o sp h eric p re ssu re (in kilopascals).

Let a = the initial p re ssu re (in kilopascals), 101.

Let b = th e decay factor, w hich is 1 - 0.115 = 0.885.

Write y = 101 • 0.885*

Use th e eq u a tio n to estim ate th e p ressure at an altitude of 3000 m.

y = 101 • 0.885*

= 101 • 0.885! Substitute 3 fo r x.

~ 70 Round to the nearest kilopascal.

The pressure at an altitude of 3000 m is ab o u t 70 kilopascals.

Got It? 3. a. W hat is th e atm o sp h eric pressure at an altitude of 5000 m?

b. Reasoning Why do you subtract the p ercen t d ecrease from 1 to find the

decay factor?

Lesso n Ch eck

Do y o u k n o w H OW?

1. What is the growth factor in the equation y = 34 • 4*?


2. What is the initial am ount in the function y = 15 • 3*?


3. What is the decay factor in the function y = 17 • 0.2*?


4. A population of fish in a lake decreases 6% annually.
   W hat is th e decay factor?


5. Suppose your friend’s paren ts invest $20,000 in an
   account paying 5% interest c o m p o u n d ed annually.
   W hat will th e balance be after 10 yr?

_ MATHEMATICAL

Do yo u UN DERSTAND? PRACTICES

6. V o c a b u l a r y How can you tell if an exponential

function m odels grow th or decay?

7. Reasoning How can you simplify the compound
   interest form ula w h en th e interest is com pounded
   annually? Explain.


8. E r r o r A n a l y s i s A stu d en t deposits $500 into an
   acco u n t th a t earns 3.5% interest com p o u n d ed
   quarterly. D escribe an d correct th e stu d e n t’s error
   in calculating th e acco u n t balance after 2 yr.

c

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