The graph of 𝑓(𝑥) passes through the point (0,4). The slope of 𝑓 at any point 𝑃 is 4 times the 𝑦−coordinate of 𝑃. Find 𝑓(1). 𝑓(1)=

Answer 1

dy/dx=4y

dy/y = 4 dx

ln y = 4x + C

y=Ke^4x

Since y = 4 when x = 0, K=4

and y=4e⁴ when x = 1