Question

The function f is given by f(x)=10x+3 and the function g is given by g(x)=2ˣ . For each question, show your reasoning.

Which function reaches 50 first?

Answer 1

The function f(x) = 10x + 3 reaches the value of 50 when x is 4.7, while the function g(x) = 2^x reaches 50 when x is approximately 5.64. Therefore, f(x) reaches 50 first.

Step-by-step explanation:

To determine which function reaches 50 first, we'll set each function equal to 50 and solve for x.

For the function f(x) = 10x + 3:
50 = 10x + 3
47 = 10x
x = 4.7

For the function g(x) = 2x:
50 = 2x
To solve this, we take the logarithm of both sides:
log(50) = x * log(2)
x = log(50) / log(2)
x ≈ 5.64

The function f(x) reaches 50 when x is 4.7, whereas the function g(x) reaches 50 when x is approximately 5.64. Therefore, the function f(x) reaches the value of 50 first.