Question

Write an exponential function in the form y = ab^x that goes through points (0,20) and (2,320).

Answer 1

Answer:

y = 20*4^x

Step-by-step explanation:

to find the value of the constants a and b, we just need to use the points given in the equation and solve the system of equations:

point (0,20): x = 0 and y = 20:

20 = a*b^0 = a*1 = a

a = 20

point (2,320): x = 2 and y = 320

320 = 20 * b^2

b^2 = 16

|b| = 4

b = 4 or b = -4

So we have two exponencial equations that pass through these points:

y = 20*4^x and y = 20*(-4)^x

As the questions asks for just one equation, we can answer y = 20*4^x

Answer 2

Answer:

The exponential function is;

$y = a \cdot b^x$

Step-by-step explanation:

Here we have;

y = ab^x

Therefore for points (0, 20) we have

20 = a·b⁰ = a

∴ a = 20

For point (2, 320) we have;

320 = 20×b²

Therefore, b² = 320/20 = 16

Hence b = √16 = 4

From the above, the exponential function y = a·b^x is given by substituting the values of a and b as follows;

y = 20×4^x.