Question

The exponential function f, represented in the table, can be written as

Answer 1

Answer:

$f(x) = 9 \bigg(\frac{5}{3} \bigg)^x$

Step-by-step explanation:

Note the f(0) = 9

and f(1) = 15

Since, f(x) = abˣ substituting for x, we get:

9 = f(0) = a . b⁰ = a

⇒ a = 9

Now, f(1) = 15

⇒ 15 = a . b¹

⇒ 15 = 9 . b

⇒ b = $\frac{15}{9}$

Therefore, $f(x) = 9 . \bigg( \frac{5}{3} \bigg) ^x$

Hence, the answer.