Precalculus question

Question

Find a formula for the exponential function of the form  that passes through the points (-2, ) and (3,320)

y=__?

Answer 1

5/16 = ab^-2

320 = ab³

1024 = b⁵ Divide second equation by first

4 = b

Now substitute 4 for b in either equation to determine a.

Answer 2

5/16 = ab^-2

320 = ab^3

from 1st equation:

5/16 = ab^-2

5b^2

------- = a

16

substitute for a in second equation

320 = 5b^2b^3

------------

16

5120 = 5b^5

1024 = b^5

b = 4

substitute value for b in 2nd equation

320 = ab^3

320 = a4^3

320 = a* 64

a = 5

f(x) = ab^x

f(x) = 5*4^x