^ Challenge Solve each equation.
- 2 = 64 52. 3x = i 53. 3 - 2 = 24 54. 5 • 2X - 152 = 8
- Suppose (0, 4) an d (2, 36) are on th e graph of an exponential function.
a. Use (0, 4) in th e general form of an exponential function, y = a • bx, to find the
value of the constant a.
b. Use your answ er from p a rt (a) an d (2, 36) to find th e value of th e co n stan t b.
c. Write a rule for th e function.
d. Evaluate th e function for x = - 2 an d x — 4.
Apply What You've Learned
MATHEMATICAL
PRACTICES
MP 7
Look back at th e inform ation on page 417 a b o u t th e two CDs th a t Em ilio is
considering for the investm ent of his prize m oney, a n d at your w ork in the
Apply W hat You’ve L earned in Lesson 7-3.
Let r be the an n u a l interest rate, expressed as a decim al, of an account for
w hich interest is co m p o u n d ed n tim e s p e r year, a n d le t P r e p r e s e n t t h e s t a r t i n g
principal (the initial deposit).
a. W rite an expression in term s of r a n d n for th e interest rate u sed to calculate the
interest for each com pounding period.
b. Write an expression in term s of P, r, and n for th e value of th e acco u n t after the first
compounding period.c. Explain how you can use the Distributive P roperty to rew rite your expression from
p art (b).
d. Using a process sim ilar to the one you u sed to com plete the table on page 438,
you can show th a t th e form ula A = P (1 + ^ j gives th e value of th e ac co u n t after
x com po u n d in g periods. Use this form ula to confirm your result in p a rt (b) of the
Apply W hat You’ve L earned on page 438.
e. Suppose Emilio chooses th e First Bank CD. Use th e form ula given in p a rt (d) to find
th e value of th e CD after one year.
f. Is th e form ula given in p a rt (d) an exponential function? Explain.