1 Let 2a 5 and 2b 11 Using exponent rules solve the equati

1) Let 2^a = 5 and 2^b = 11. Using exponent rules, solve the equation 12.8^x = 121 in terms of a and b.

x =____________

2) Find a formula for f(x) , an exponential function such that f(2)=127 and f(-1)=27.

f(x) = ___________

a = 256

k = ___________

2) f(2) = 1/27 ; f(-1) = 27

f(x) =ae^kx

1/27 = ae^2k ----(1)

27 = ae^-k ----(2)

divide both equations : 27*27 =e^-3k

e^3k = 1/27*27

take cube root on both sides: e^k = 1/9

1/27 = ae^2k

= a(e^k)^2

1/27 = a(1/9)^2

a = 81/27 = 9/3 = 3

So, f(x) = 3e^kt

= 3(1/9)^x

f(x) = 3(9)^-x

3) P(t) = (4 *7th root (e^4t))^4

applying exponent property

7th root can be written as raised to power 1/7

P(t) = 4^4 (e^4t)^1/7*4

P(t) = 256 e^4t*4/7 = 256 e^16t/7

a = 256

k = 16/7